Solve 9+m^2=1+(m+4)^2

$$9 + m ^ { 2 } = 1 + ( m + 4 ) ^ { 2 }$$

Solve for m

$$m=-1$$

Steps for Solving Linear Equation

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

$$9+m^{2}=1+m^{2}+8m+16$$

Add 1 and 16 to get 17.

$$9+m^{2}=17+m^{2}+8m$$

Subtract m^{2} from both sides.

$$9+m^{2}-m^{2}=17+8m$$

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

$$9=17+8m$$

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

$$17+8m=9$$

Subtract 17 from both sides.

$$8m=9-17$$

Subtract 17 from 9 to get -8.

$$8m=-8$$

Divide both sides by 8.

$$m=\frac{-8}{8}$$

Divide -8 by 8 to get -1.

$$m=-1$$