Solve x^2+3x+9=(x+2)^2-17

$$x ^ { 2 } + 3 x + 9 = ( x + 2 ) ^ { 2 } - 17$$

Solve for x

$$x=22$$

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}.

$$x^{2}+3x+9=x^{2}+4x+4-17$$

Subtract 17 from 4 to get -13.

$$x^{2}+3x+9=x^{2}+4x-13$$

Subtract x^{2} from both sides.

$$x^{2}+3x+9-x^{2}=4x-13$$

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

$$3x+9=4x-13$$

Subtract 4x from both sides.

$$3x+9-4x=-13$$

Combine 3x and -4x to get -x.

$$-x+9=-13$$

Subtract 9 from both sides.

$$-x=-13-9$$

Subtract 9 from -13 to get -22.

$$-x=-22$$

Multiply both sides by -1.

$$x=22$$