== 平方完成の基本 ==

== 難易などの目安 ==
《考え方》
　　★：易しい，★★：普通，★★★：難しい
《計算量》
　　☆：少ない，☆☆：普通，☆☆☆：多い
　⇒　教科書レベル

∃∀ ∅==楽しくやろうぜ！？==♣♥♦
　空欄?に入る数字を下の選択肢から１つ選んで，マウスでクリック（携帯の場合は，指でタップ）してください．正しければ，代入されます．間違っていれば，やり直しできます．
【問１】
(1)　\(x^2+4x=(x+\)?\()^2\hspace{15px}-\hspace{15px}\)?
01
234
567
89
01
4916
253649
6481

解答を見る ⇒
(2)　\(x^2-6x=(x-\)?\()^2\hspace{15px}-\hspace{15px}\)?
01
234
567
89
01
4916
253649
6481

解答を見る ⇒
(3)　\(x^2+8x=(x+\)?\()^2\hspace{15px}-\hspace{15px}\)?
01
234
567
89
01
4916
253649
6481

解答を見る ⇒

【問２】
(1)　\(x^2-2x+3=(x-\)?\()^2\hspace{15px}+\hspace{15px}\)?
01
234
567
89
01
234
567
89

解答を見る ↓
(2)　\(x^2+6x+3=(x+\)?\()^2\hspace{15px}-\hspace{15px}\)?
01
234
567
89
01
234
567
89

解答を見る ↓
(3)　\(x^2-10x+5=(x-\)?\()^2\hspace{15px}-\hspace{15px}\)?
01
234
567
89
12
3510
121516
2025

解答を見る ↓

【問３】
(1)　\(x^2-3x=(x-\)?\()^2\hspace{15px}-\hspace{15px}\)?
\(\small 1\)\(\small \displaystyle \frac{1}{2}\)
2\(\small \displaystyle \frac{3}{2}\)\(\small \displaystyle 2\)
\(\small \displaystyle \frac{5}{2}\)\(\small \displaystyle 3\)\(\small \displaystyle \frac{7}{2}\)
\(\small \displaystyle 4\)\(\small \displaystyle \frac{9}{2}\)
\(\small \displaystyle 0\)\(\small \displaystyle \frac{1}{4}\)
\(\small \displaystyle \frac{1}{2}\)\(\small \displaystyle \frac{3}{4}\)\(\small \displaystyle 1\)
\(\small \displaystyle \frac{5}{4}\)\(\small \displaystyle \frac{3}{2}\)\(\small \displaystyle \frac{7}{4}\)
\(\small \displaystyle 4\)\(\small \displaystyle \frac{9}{4}\)

解答を見る ↓
(2)　\(x^2+x=(x+\)?\()^2\hspace{15px}-\hspace{15px}\)?
\(\small 1\)\(\small \displaystyle \frac{1}{2}\)
2\(\small \displaystyle \frac{3}{2}\)\(\small \displaystyle 2\)
\(\small \displaystyle \frac{5}{2}\)\(\small \displaystyle 3\)\(\small \displaystyle \frac{7}{2}\)
\(\small \displaystyle 4\)\(\small \displaystyle \frac{9}{2}\)
\(\small \displaystyle 0\)\(\small \displaystyle \frac{1}{4}\)
\(\small \displaystyle \frac{1}{2}\)\(\small \displaystyle \frac{3}{4}\)\(\small \displaystyle 1\)
\(\small \displaystyle \frac{5}{4}\)\(\small \displaystyle \frac{3}{2}\)\(\small \displaystyle \frac{7}{4}\)
\(\small \displaystyle 4\)\(\small \displaystyle \frac{9}{4}\)

解答を見る ↓
(3)　\(x^2-5x=(x-\)?\()^2\hspace{15px}-\hspace{15px}\)?
\(\small 1\)\(\small \displaystyle \frac{1}{2}\)
2\(\small \displaystyle \frac{3}{2}\)\(\small \displaystyle 2\)
\(\small \displaystyle \frac{5}{2}\)\(\small \displaystyle 3\)\(\small \displaystyle \frac{7}{2}\)
\(\small \displaystyle 4\)\(\small \displaystyle \frac{9}{2}\)
\(\small \displaystyle \frac{1}{2}\)\(\small \displaystyle \frac{1}{4}\)
\(\small \displaystyle \frac{3}{2}\)\(\small \displaystyle \frac{3}{4}\)\(\small \displaystyle \frac{7}{2}\)
\(\small \displaystyle \frac{7}{4}\)\(\small \displaystyle \frac{9}{2}\)\(\small \displaystyle \frac{9}{4}\)
\(\small \displaystyle \frac{25}{2}\)\(\small \displaystyle \frac{25}{4}\)

解答を見る ↓

【問４】
(1)　\(x^2+7x+1=(x+\)?\()^2\hspace{15px}-\hspace{15px}\)?
\(\small 1\)\(\small \displaystyle \frac{1}{2}\)
2\(\small \displaystyle \frac{3}{2}\)\(\small \displaystyle 2\)
\(\small \displaystyle \frac{5}{2}\)\(\small \displaystyle 3\)\(\small \displaystyle \frac{7}{2}\)
\(\small \displaystyle 4\)\(\small \displaystyle \frac{9}{2}\)
\(\small \displaystyle 0\)\(\small \displaystyle \frac{3}{2}\)
\(\small \displaystyle \frac{5}{2}\)\(\small \displaystyle \frac{7}{2}\)\(\small \displaystyle \frac{7}{4}\)
\(\small \displaystyle \frac{41}{4}\)\(\small \displaystyle \frac{43}{4}\)\(\small \displaystyle \frac{45}{4}\)
\(\small \displaystyle \frac{47}{4}\)\(\small \displaystyle \frac{49}{4}\)

解答を見る ↓
(2)　\(x^2-9x-2=(x-\)?\()^2\hspace{15px}-\hspace{15px}\)?
\(\small 1\)\(\small \displaystyle \frac{1}{2}\)
2\(\small \displaystyle \frac{3}{2}\)\(\small \displaystyle 2\)
\(\small \displaystyle \frac{5}{2}\)\(\small \displaystyle 3\)\(\small \displaystyle \frac{7}{2}\)
\(\small \displaystyle 4\)\(\small \displaystyle \frac{9}{2}\)
\(\small \displaystyle \frac{3}{2}\)\(\small \displaystyle \frac{5}{2}\)
\(\small \displaystyle \frac{7}{2}\)\(\small \displaystyle \frac{9}{2}\)\(\small \displaystyle \frac{75}{4}\)
\(\small \displaystyle \frac{77}{4}\)\(\small \displaystyle \frac{79}{4}\)\(\small \displaystyle \frac{81}{4}\)
\(\small \displaystyle \frac{83}{4}\)\(\small \displaystyle \frac{89}{4}\)

解答を見る ↓
(3)　\(x^2+3x+3=(x+\)?\()^2\hspace{15px}+\hspace{15px}\)?
\(\small 1\)\(\small \displaystyle \frac{1}{2}\)
2\(\small \displaystyle \frac{3}{2}\)\(\small \displaystyle 2\)
\(\small \displaystyle \frac{5}{2}\)\(\small \displaystyle 3\)\(\small \displaystyle \frac{7}{2}\)
\(\small \displaystyle 4\)\(\small \displaystyle \frac{9}{2}\)
\(\small \displaystyle 1\)\(\small \displaystyle 2\)
\(\small \displaystyle 3\)\(\small \displaystyle \frac{5}{2}\)\(\small \displaystyle \frac{7}{2}\)
\(\small \displaystyle \frac{1}{4}\)\(\small \displaystyle \frac{3}{4}\)\(\small \displaystyle \frac{5}{4}\)
\(\small \displaystyle \frac{7}{4}\)\(\small \displaystyle \frac{9}{4}\)

解答を見る ↓

【問５】

♪♬∃==楽しくやろうぜ！？==♫♠♣
(1)　\(2x^2+10x\)
\(=\)? \((x+\)? \()^2\hspace{35px}-\hspace{35px}\)?
\(\small 1\)\(\small \displaystyle 2\)
\(\small 3\)\(\small \displaystyle 4\)\(\small \displaystyle 5\)
\(\small \displaystyle 6\)\(\small \displaystyle 7\)\(\small \displaystyle 8\)
\(\small \displaystyle 9\)\(\small \displaystyle 10\)
\(\small \displaystyle 0\)\(\small \displaystyle \frac{3}{2}\)
\(\small \displaystyle \frac{5}{2}\)\(\small \displaystyle \frac{7}{2}\)\(\small \displaystyle \frac{7}{4}\)
\(\small \displaystyle \frac{41}{4}\)\(\small \displaystyle \frac{43}{4}\)\(\small \displaystyle \frac{45}{4}\)
\(\small \displaystyle \frac{47}{4}\)\(\small \displaystyle \frac{49}{4}\)
\(\small \displaystyle \frac{1}{2}\)\(\small \displaystyle \frac{7}{2}\)
\(\small \displaystyle \frac{9}{2}\)\(\small \displaystyle \frac{17}{2}\)\(\small \displaystyle \frac{25}{2}\)
\(\small \displaystyle \frac{7}{4}\)\(\small \displaystyle \frac{13}{4}\)\(\small \displaystyle \frac{25}{4}\)
\(\small \displaystyle \frac{37}{4}\)\(\small \displaystyle \frac{49}{4}\)

解答を見る ↓
(2)　\(3x^2-2x\)
\(=\)? \((x-\)? \()^2\hspace{35px}-\hspace{35px}\)?
\(\small 1\)\(\small \displaystyle 2\)
\(\small 3\)\(\small \displaystyle 4\)\(\small \displaystyle 5\)
\(\small \displaystyle 6\)\(\small \displaystyle 7\)\(\small \displaystyle 8\)
\(\small \displaystyle 9\)\(\small \displaystyle 10\)
\(\small \displaystyle \frac{1}{6}\)\(\small \displaystyle \frac{1}{3}\)
\(\small \displaystyle \frac{5}{6}\)\(\small \displaystyle \frac{2}{3}\)\(\small \displaystyle \frac{4}{3}\)
\(\small \displaystyle \frac{1}{9}\)\(\small \displaystyle \frac{2}{9}\)\(\small \displaystyle \frac{4}{9}\)
\(\small \displaystyle \frac{5}{9}\)\(\small \displaystyle \frac{7}{9}\)
\(\small \displaystyle \frac{1}{2}\)\(\small \displaystyle \frac{3}{2}\)
\(\small \displaystyle \frac{5}{2}\)\(\small \displaystyle \frac{1}{3}\)\(\small \displaystyle \frac{2}{3}\)
\(\small \displaystyle \frac{4}{3}\)\(\small \displaystyle \frac{1}{6}\)\(\small \displaystyle \frac{1}{9}\)
\(\small \displaystyle \frac{2}{9}\)\(\small \displaystyle \frac{5}{9}\)

解答を見る ↓
(3)　\(5x^2+4x\)
\(=\)? \((x+\)? \()^2\hspace{35px}-\hspace{35px}\)?
\(\small 1\)\(\small \displaystyle 2\)
\(\small 3\)\(\small \displaystyle 4\)\(\small \displaystyle 5\)
\(\small \displaystyle 6\)\(\small \displaystyle 7\)\(\small \displaystyle 8\)
\(\small \displaystyle 9\)\(\small \displaystyle 10\)
\(\small \displaystyle \frac{1}{5}\)\(\small \displaystyle \frac{2}{5}\)
\(\small \displaystyle \frac{3}{5}\)\(\small \displaystyle \frac{4}{5}\)\(\small \displaystyle \frac{1}{25}\)
\(\small \displaystyle \frac{2}{25}\)\(\small \displaystyle \frac{3}{25}\)\(\small \displaystyle \frac{4}{25}\)
\(\small \displaystyle \frac{6}{25}\)\(\small \displaystyle \frac{9}{25}\)
\(\small \displaystyle \frac{1}{5}\)\(\small \displaystyle \frac{2}{5}\)
\(\small \displaystyle \frac{3}{5}\)\(\small \displaystyle \frac{4}{5}\)\(\small \displaystyle \frac{1}{25}\)
\(\small \displaystyle \frac{2}{25}\)\(\small \displaystyle \frac{3}{25}\)\(\small \displaystyle \frac{5}{25}\)
\(\small \displaystyle \frac{7}{25}\)\(\small \displaystyle \frac{9}{25}\)

解答を見る ↓

【問６】
(1)　\(2x^2+8x+5\)
\(=\)? \((x+\)? \()^2\hspace{35px}-\hspace{35px}\)?
\(\small 1\)\(\small \displaystyle 2\)
\(\small 3\)\(\small \displaystyle 4\)\(\small \displaystyle 5\)
\(\small \displaystyle 6\)\(\small \displaystyle 7\)\(\small \displaystyle 8\)
\(\small \displaystyle 9\)\(\small \displaystyle 10\)
\(\small \displaystyle 1\)\(\small \displaystyle 2\)
\(\small \displaystyle 3\)\(\small \displaystyle 4\)\(\small \displaystyle 5\)
\(\small \displaystyle 6\)\(\small \displaystyle 7\)\(\small \displaystyle 8\)
\(\small \displaystyle \frac{1}{2}\)\(\small \displaystyle \frac{1}{4}\)
\(\small \displaystyle 1\)\(\small \displaystyle 2\)
\(\small \displaystyle 3\)\(\small \displaystyle 4\)\(\small \displaystyle 5\)
\(\small \displaystyle 6\)\(\small \displaystyle 7\)\(\small \displaystyle 8\)
\(\small \displaystyle \frac{1}{2}\)\(\small \displaystyle \frac{1}{4}\)

解答を見る ↓
(2)　\(-3x^2+5x-1\)
\(=\)? \((x-\)? \()^2\hspace{25px}+\hspace{25px}\)?
\(\small -5\)\(\small \displaystyle -4\)
\(\small -3\)\(\small \displaystyle -2\)\(\small \displaystyle -1\)
\(\small \displaystyle 1\)\(\small \displaystyle 2\)\(\small \displaystyle 3\)
\(\small \displaystyle 4\)\(\small \displaystyle 5\)
\(\small \displaystyle \frac{1}{2}\)\(\small \displaystyle \frac{3}{2}\)
\(\small \displaystyle \frac{1}{3}\)\(\small \displaystyle \frac{2}{3}\)\(\small \displaystyle \frac{5}{3}\)
\(\small \displaystyle \frac{1}{6}\)\(\small \displaystyle\frac{5}{6}\)\(\small \displaystyle \frac{1}{9}\)
\(\small \displaystyle \frac{2}{9}\)\(\small \displaystyle \frac{5}{9}\)
\(\small \displaystyle \frac{1}{3}\)\(\small \displaystyle \frac{2}{3}\)
\(\small \displaystyle \frac{4}{3}\)\(\small \displaystyle \frac{1}{6}\)\(\small \displaystyle \frac{5}{6}\)
\(\small \displaystyle \frac{7}{6}\)\(\small \displaystyle \frac{5}{12}\)\(\small \displaystyle \frac{7}{12}\)
\(\small \displaystyle \frac{11}{12}\)\(\small \displaystyle \frac{13}{12}\)

解答を見る ↓
(3)　\(5x^2+3x-2\)
\(=\)? \((x+\)? \()^2\hspace{25px}-\hspace{25px}\)?
\(\small -5\)\(\small \displaystyle -4\)
\(\small -3\)\(\small \displaystyle -2\)\(\small \displaystyle -1\)
\(\small \displaystyle 1\)\(\small \displaystyle 2\)\(\small \displaystyle 3\)
\(\small \displaystyle 4\)\(\small \displaystyle 5\)
\(\small \displaystyle \frac{3}{2}\)\(\small \displaystyle \frac{5}{2}\)
\(\small \displaystyle \frac{3}{5}\)\(\small \displaystyle \frac{6}{5}\)\(\small \displaystyle \frac{3}{10}\)
\(\small \displaystyle \frac{9}{10}\)\(\small \displaystyle\frac{3}{20}\)\(\small \displaystyle \frac{9}{20}\)
\(\small \displaystyle \frac{3}{100}\)\(\small \displaystyle \frac{9}{100}\)
\(\small \displaystyle \frac{9}{10}\)\(\small \displaystyle \frac{49}{10}\)
\(\small \displaystyle \frac{9}{20}\)\(\small \displaystyle \frac{49}{20}\)\(\small \displaystyle \frac{9}{25}\)
\(\small \displaystyle \frac{3}{100}\)\(\small \displaystyle \frac{9}{100}\)\(\small \displaystyle \frac{3}{5}\)
\(\small \displaystyle \frac{9}{5}\)\(\small \displaystyle \frac{49}{5}\)

解答を見る ↓

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