Solve (x+2)^2=(sqrt{x^2+1})^2

$$( x + 2 ) ^ { 2 } = ( \sqrt { x ^ { 2 } + 1 } ) ^ { 2 }$$

Solve for x

$$x=-\frac{3}{4}=-0.75$$

Steps for Solving Linear Equation

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

$$x^{2}+4x+4=\left(\sqrt{x^{2}+1}\right)^{2}$$

Calculate \sqrt{x^{2}+1} to the power of 2 and get x^{2}+1.

$$x^{2}+4x+4=x^{2}+1$$

Subtract x^{2} from both sides.

$$x^{2}+4x+4-x^{2}=1$$

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

$$4x+4=1$$

Subtract 4 from both sides.

$$4x=1-4$$

Subtract 4 from 1 to get -3.

$$4x=-3$$

Divide both sides by 4.

$$x=\frac{-3}{4}$$

Fraction \frac{-3}{4} can be rewritten as -\frac{3}{4} by extracting the negative sign.

$$x=-\frac{3}{4}$$