Solve (8-a)^2-a^2-8/8=1/2

$$\frac { ( 8 - a ) ^ { 2 } - a ^ { 2 } - 8 } { 8 } = \frac { 1 } { 2 }$$

Solve for a

$$a = \frac{13}{4} = 3\frac{1}{4} = 3.25$$

Steps for Solving Linear Equation

Multiply both sides by 8.

$$\left(8-a\right)^{2}-a^{2}-8=\frac{1}{2}\times 8$$

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

$$64-16a+a^{2}-a^{2}-8=\frac{1}{2}\times 8$$

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

$$64-16a-8=\frac{1}{2}\times 8$$

Subtract 8 from 64 to get 56.

$$56-16a=\frac{1}{2}\times 8$$

Multiply \frac{1}{2} and 8 to get 4.

$$56-16a=4$$

Subtract 56 from both sides.

$$-16a=4-56$$

Subtract 56 from 4 to get -52.

$$-16a=-52$$

Divide both sides by -16.

$$a=\frac{-52}{-16}$$

Reduce the fraction \frac{-52}{-16} to lowest terms by extracting and canceling out -4.

$$a=\frac{13}{4}$$