置き換えを使う2次方程式

(7x-5)²-7x+5=12 (200-3x)(203-3x)=208-3x 30000x²-800x+5=0 解説動画 ≫ (7x-5)²-7x+5=12
(7x-5)²-(7x-5)-12=0　　↓7x-5=Aとおく
A²-A-12=0
(A+3)(A-4)=0
(7x-5+3)(7x-5-4)=0
(7x-2)(7x-9)=0
x = 97,27 (200-3x)(203-3x)=208-3x　　↓200-3x=Aとおく
A(A+3) = A+8
A²+3A-A-8=0
A²+2A-8=0
(A-2)(A+4)=0
(200-3x-2)(200-3x+4)=0
(198-3x)(204-3x)=0
3x=198 , 3x=204
x = 66, 68 30000x²-800x+5=0
3(100x)²-8(100x)+5=0　　↓100x=Aとおく
3A²-8A+5=0
A=-(-8)±(-8)²-4×3×52×3
=8±26
=1,53
100x=1,100x=53
x=1100,160

【練習】
答表示
(2x+9)²+2(2x+9)-15=0
x = -3, -7 (4x-7)²-4x+7=6
x = 52,54 (130-x)(131-x)=139-x
x = 133,127 (90-5x)(92-5x)=96-5x
x = 935,885 10000x²-600x+7=0
x = 3±2100