Solve (x-1)^2=(x-7)(x+7)

$$( x - 1 ) ^ { 2 } = ( x - 7 ) ( x + 7 )$$

Solve for x

$$x=25$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

$$x^{2}-2x+1=\left(x-7\right)\left(x+7\right)$$

Consider \left(x-7\right)\left(x+7\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 7.

$$x^{2}-2x+1=x^{2}-49$$

Subtract x^{2} from both sides.

$$x^{2}-2x+1-x^{2}=-49$$

Combine x^{2} and -x^{2} to get 0.

$$-2x+1=-49$$

Subtract 1 from both sides.

$$-2x=-49-1$$

Subtract 1 from -49 to get -50.

$$-2x=-50$$

Divide both sides by -2.

$$x=\frac{-50}{-2}$$

Divide -50 by -2 to get 25.

$$x=25$$