Solve (x+5)^2=x^2+5x+115

$$( x + 5 ) ^ { 2 } = x ^ { 2 } + 5 x + 115$$

Solve for x

$$x=18$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+5\right)^{2}.

$$x^{2}+10x+25=x^{2}+5x+115$$

Subtract x^{2} from both sides.

$$x^{2}+10x+25-x^{2}=5x+115$$

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

$$10x+25=5x+115$$

Subtract 5x from both sides.

$$10x+25-5x=115$$

Combine 10x and -5x to get 5x.

$$5x+25=115$$

Subtract 25 from both sides.

$$5x=115-25$$

Subtract 25 from 115 to get 90.

$$5x=90$$

Divide both sides by 5.

$$x=\frac{90}{5}$$

Divide 90 by 5 to get 18.

$$x=18$$