Solve x^2=(x+4)^2+3^2

$$x ^ { 2 } = ( x + 4 ) ^ { 2 } + 3 ^ { 2 }$$

Solve for x

$$x = -\frac{25}{8} = -3\frac{1}{8} = -3.125$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+4\right)^{2}.

$$x^{2}=x^{2}+8x+16+3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$x^{2}=x^{2}+8x+16+9$$

Add 16 and 9 to get 25.

$$x^{2}=x^{2}+8x+25$$

Subtract x^{2} from both sides.

$$x^{2}-x^{2}=8x+25$$

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

$$0=8x+25$$

Swap sides so that all variable terms are on the left hand side.

$$8x+25=0$$

Subtract 25 from both sides. Anything subtracted from zero gives its negation.

$$8x=-25$$

Divide both sides by 8.

$$x=\frac{-25}{8}$$

Fraction \frac{-25}{8} can be rewritten as -\frac{25}{8} by extracting the negative sign.

$$x=-\frac{25}{8}$$