Solve a^2/4=(a/2+2)^2-8^2

$$\frac { a ^ { 2 } } { 4 } = ( \frac { a } { 2 } + 2 ) ^ { 2 } - 8 ^ { 2 }$$

Solve for a

$$a=30$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4.

$$a^{2}=4\left(\frac{a}{2}+2\right)^{2}-4\times 8^{2}$$

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

$$a^{2}=4\left(\left(\frac{a}{2}\right)^{2}+4\times \frac{a}{2}+4\right)-4\times 8^{2}$$

To raise \frac{a}{2} to a power, raise both numerator and denominator to the power and then divide.

$$a^{2}=4\left(\frac{a^{2}}{2^{2}}+4\times \frac{a}{2}+4\right)-4\times 8^{2}$$

Cancel out 2, the greatest common factor in 4 and 2.

$$a^{2}=4\left(\frac{a^{2}}{2^{2}}+2a+4\right)-4\times 8^{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2a+4 times \frac{2^{2}}{2^{2}}.

$$a^{2}=4\left(\frac{a^{2}}{2^{2}}+\frac{\left(2a+4\right)\times 2^{2}}{2^{2}}\right)-4\times 8^{2}$$

Since \frac{a^{2}}{2^{2}} and \frac{\left(2a+4\right)\times 2^{2}}{2^{2}} have the same denominator, add them by adding their numerators.

$$a^{2}=4\times \frac{a^{2}+\left(2a+4\right)\times 2^{2}}{2^{2}}-4\times 8^{2}$$

Do the multiplications in a^{2}+\left(2a+4\right)\times 2^{2}.

$$a^{2}=4\times \frac{a^{2}+8a+16}{2^{2}}-4\times 8^{2}$$

Express 4\times \frac{a^{2}+8a+16}{2^{2}} as a single fraction.

$$a^{2}=\frac{4\left(a^{2}+8a+16\right)}{2^{2}}-4\times 8^{2}$$

Calculate 8 to the power of 2 and get 64.

$$a^{2}=\frac{4\left(a^{2}+8a+16\right)}{2^{2}}-4\times 64$$

Multiply 4 and 64 to get 256.

$$a^{2}=\frac{4\left(a^{2}+8a+16\right)}{2^{2}}-256$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 256 times \frac{2^{2}}{2^{2}}.

$$a^{2}=\frac{4\left(a^{2}+8a+16\right)}{2^{2}}-\frac{256\times 2^{2}}{2^{2}}$$

Since \frac{4\left(a^{2}+8a+16\right)}{2^{2}} and \frac{256\times 2^{2}}{2^{2}} have the same denominator, subtract them by subtracting their numerators.

$$a^{2}=\frac{4\left(a^{2}+8a+16\right)-256\times 2^{2}}{2^{2}}$$

Do the multiplications in 4\left(a^{2}+8a+16\right)-256\times 2^{2}.

$$a^{2}=\frac{4a^{2}+32a+64-1024}{2^{2}}$$

Combine like terms in 4a^{2}+32a+64-1024.

$$a^{2}=\frac{4a^{2}+32a-960}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$a^{2}=\frac{4a^{2}+32a-960}{4}$$

Divide each term of 4a^{2}+32a-960 by 4 to get -240+8a+a^{2}.

$$a^{2}=-240+8a+a^{2}$$

Subtract 8a from both sides.

$$a^{2}-8a=-240+a^{2}$$

Subtract a^{2} from both sides.

$$a^{2}-8a-a^{2}=-240$$

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

$$-8a=-240$$

Divide both sides by -8.

$$a=\frac{-240}{-8}$$

Divide -240 by -8 to get 30.

$$a=30$$