Solve m^2+(m+4)^2=(m+8/5)^2+(m+27/5)^2

$$m ^ { 2 } + ( m + 4 ) ^ { 2 } = ( m + \frac { 8 } { 5 } ) ^ { 2 } + ( m + \frac { 27 } { 5 } ) ^ { 2 }$$

Solve for m

$$m = -\frac{131}{50} = -2\frac{31}{50} = -2.62$$

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}.

$$m^{2}+m^{2}+8m+16=\left(m+\frac{8}{5}\right)^{2}+\left(m+\frac{27}{5}\right)^{2}$$

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

$$2m^{2}+8m+16=\left(m+\frac{8}{5}\right)^{2}+\left(m+\frac{27}{5}\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(m+\frac{8}{5}\right)^{2}.

$$2m^{2}+8m+16=m^{2}+\frac{16}{5}m+\frac{64}{25}+\left(m+\frac{27}{5}\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(m+\frac{27}{5}\right)^{2}.

$$2m^{2}+8m+16=m^{2}+\frac{16}{5}m+\frac{64}{25}+m^{2}+\frac{54}{5}m+\frac{729}{25}$$

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

$$2m^{2}+8m+16=2m^{2}+\frac{16}{5}m+\frac{64}{25}+\frac{54}{5}m+\frac{729}{25}$$

Combine \frac{16}{5}m and \frac{54}{5}m to get 14m.

$$2m^{2}+8m+16=2m^{2}+14m+\frac{64}{25}+\frac{729}{25}$$

Add \frac{64}{25} and \frac{729}{25} to get \frac{793}{25}.

$$2m^{2}+8m+16=2m^{2}+14m+\frac{793}{25}$$

Subtract 2m^{2} from both sides.

$$2m^{2}+8m+16-2m^{2}=14m+\frac{793}{25}$$

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

$$8m+16=14m+\frac{793}{25}$$

Subtract 14m from both sides.

$$8m+16-14m=\frac{793}{25}$$

Combine 8m and -14m to get -6m.

$$-6m+16=\frac{793}{25}$$

Subtract 16 from both sides.

$$-6m=\frac{793}{25}-16$$

Subtract 16 from \frac{793}{25} to get \frac{393}{25}.

$$-6m=\frac{393}{25}$$

Divide both sides by -6.

$$m=\frac{\frac{393}{25}}{-6}$$

Express \frac{\frac{393}{25}}{-6} as a single fraction.

$$m=\frac{393}{25\left(-6\right)}$$

Multiply 25 and -6 to get -150.

$$m=\frac{393}{-150}$$

Reduce the fraction \frac{393}{-150} to lowest terms by extracting and canceling out 3.

$$m=-\frac{131}{50}$$