Solve (m-3)^2=m^2+2

$$( m - 3 ) ^ { 2 } = m ^ { 2 } + 2$$

Solve for m

$$m = \frac{7}{6} = 1\frac{1}{6} \approx 1.166666667$$

Steps for Solving Linear Equation

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

$$m^{2}-6m+9=m^{2}+2$$

Subtract m^{2} from both sides.

$$m^{2}-6m+9-m^{2}=2$$

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

$$-6m+9=2$$

Subtract 9 from both sides.

$$-6m=2-9$$

Subtract 9 from 2 to get -7.

$$-6m=-7$$

Divide both sides by -6.

$$m=\frac{-7}{-6}$$

Fraction \frac{-7}{-6} can be simplified to \frac{7}{6} by removing the negative sign from both the numerator and the denominator.

$$m=\frac{7}{6}$$