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

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

Solve for x

$$x=-7$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+7\right)^{2}.

$$x^{2}+14x+49=\left(x+7\right)\left(x-7\right)$$

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.

$$x^{2}+14x+49=x^{2}-49$$

Subtract x^{2} from both sides.

$$x^{2}+14x+49-x^{2}=-49$$

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

$$14x+49=-49$$

Subtract 49 from both sides.

$$14x=-49-49$$

Subtract 49 from -49 to get -98.

$$14x=-98$$

Divide both sides by 14.

$$x=\frac{-98}{14}$$

Divide -98 by 14 to get -7.

$$x=-7$$