solve the quadratic equation: (x-1)^2 = (2x+7)^2

solve the quadratic equation: (x-1)^2 = (2x+7)^2

$$(x-1)^2 = (2x+7)^2 \quad | \quad \pm\sqrt{} \\ \pm(x-1)=\pm(2x+7)\\ I. +(x-1) = +(2x+7) \quad \Rightarrow \quad x-1=2x+7\\ x_1= -8\\ II. +(x-1) = -(2x+7)\quad \Rightarrow \quad x-1=-2x-7\\ x_2 = -2$$

x^2-2x+1=4x^2+28x+49

3(x^2+10x+16)=0

x^2+8x+2x+16=0

x(x+8)+2(x+8)=0

(x+8)(x+2)=0

Hence,x=-8,-2