Solve (w+3)^2+4=(w-2)^2+5w-2

$$( w + 3 ) ^ { 2 } + 4 = ( w - 2 ) ^ { 2 } + 5 w - 2$$

Solve for w

$$w = -\frac{11}{5} = -2\frac{1}{5} = -2.2$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(w+3\right)^{2}.

$$w^{2}+6w+9+4=\left(w-2\right)^{2}+5w-2$$

Add 9 and 4 to get 13.

$$w^{2}+6w+13=\left(w-2\right)^{2}+5w-2$$

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

$$w^{2}+6w+13=w^{2}-4w+4+5w-2$$

Combine -4w and 5w to get w.

$$w^{2}+6w+13=w^{2}+w+4-2$$

Subtract 2 from 4 to get 2.

$$w^{2}+6w+13=w^{2}+w+2$$

Subtract w^{2} from both sides.

$$w^{2}+6w+13-w^{2}=w+2$$

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

$$6w+13=w+2$$

Subtract w from both sides.

$$6w+13-w=2$$

Combine 6w and -w to get 5w.

$$5w+13=2$$

Subtract 13 from both sides.

$$5w=2-13$$

Subtract 13 from 2 to get -11.

$$5w=-11$$

Divide both sides by 5.

$$w=\frac{-11}{5}$$

Fraction \frac{-11}{5} can be rewritten as -\frac{11}{5} by extracting the negative sign.

$$w=-\frac{11}{5}$$