Solve 25-a^2=41-(8-a)^2

$$25 - a ^ { 2 } = 41 - ( 8 - a ) ^ { 2 }$$

Solve for a

$$a=3$$

Steps for Solving Linear Equation

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

$$25-a^{2}=41-\left(64-16a+a^{2}\right)$$

To find the opposite of 64-16a+a^{2}, find the opposite of each term.

$$25-a^{2}=41-64+16a-a^{2}$$

Subtract 64 from 41 to get -23.

$$25-a^{2}=-23+16a-a^{2}$$

Subtract 16a from both sides.

$$25-a^{2}-16a=-23-a^{2}$$

Add a^{2} to both sides.

$$25-a^{2}-16a+a^{2}=-23$$

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

$$25-16a=-23$$

Subtract 25 from both sides.

$$-16a=-23-25$$

Subtract 25 from -23 to get -48.

$$-16a=-48$$

Divide both sides by -16.

$$a=\frac{-48}{-16}$$

Divide -48 by -16 to get 3.

$$a=3$$