Solve pi-(a^2/4h+a^2+1)=1/2pia^2=

$$\pi - ( \frac { a ^ { 2 } } { 4 } h + a ^ { 2 } + 1 ) = \frac { 1 } { 2 } \pi a ^ { 2 } =$$

Solve for h

$$h=-2\pi -4+\frac{4\pi }{a^{2}}-\frac{4}{a^{2}}$$

$$a\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4, the least common multiple of 4,2.

$$4\pi -4\left(\frac{a^{2}}{4}h+a^{2}+1\right)=2\pi a^{2}$$

Express \frac{a^{2}}{4}h as a single fraction.

$$4\pi -4\left(\frac{a^{2}h}{4}+a^{2}+1\right)=2\pi a^{2}$$

Multiply both sides of the equation by 4.

$$16\pi -16\left(\frac{a^{2}h}{4}+a^{2}+1\right)=8\pi a^{2}$$

Multiply both sides of the equation by 4.

$$64\pi -4\times 16\left(\frac{a^{2}h}{4}+a^{2}+1\right)=32\pi a^{2}$$

Multiply -4 and 16 to get -64.

$$64\pi -64\left(\frac{a^{2}h}{4}+a^{2}+1\right)=32\pi a^{2}$$

Use the distributive property to multiply -64 by \frac{a^{2}h}{4}+a^{2}+1.

$$64\pi -64\times \frac{a^{2}h}{4}-64a^{2}-64=32\pi a^{2}$$

Cancel out 4, the greatest common factor in 64 and 4.

$$64\pi -16a^{2}h-64a^{2}-64=32\pi a^{2}$$

Subtract 64\pi from both sides.

$$-16a^{2}h-64a^{2}-64=32\pi a^{2}-64\pi$$

Add 64a^{2} to both sides.

$$-16a^{2}h-64=32\pi a^{2}-64\pi +64a^{2}$$

Add 64 to both sides.

$$-16a^{2}h=32\pi a^{2}-64\pi +64a^{2}+64$$

The equation is in standard form.

$$\left(-16a^{2}\right)h=32\pi a^{2}+64a^{2}+64-64\pi$$

Divide both sides by -16a^{2}.

$$\frac{\left(-16a^{2}\right)h}{-16a^{2}}=\frac{32\pi a^{2}+64a^{2}+64-64\pi }{-16a^{2}}$$

Dividing by -16a^{2} undoes the multiplication by -16a^{2}.

$$h=\frac{32\pi a^{2}+64a^{2}+64-64\pi }{-16a^{2}}$$

Divide 32\pi a^{2}-64\pi +64a^{2}+64 by -16a^{2}.

$$h=-2\pi -4+\frac{4\pi -4}{a^{2}}$$

Solve for a (complex solution)

$$a=2\sqrt{\pi -1}\left(h+2\pi +4\right)^{-\frac{1}{2}}$$

$$a=-2\sqrt{\pi -1}\left(h+2\pi +4\right)^{-\frac{1}{2}}\text{, }h\neq -2\pi -4$$

Solve for a

$$a=2\sqrt{\frac{\pi -1}{h+2\pi +4}}$$

$$a=-2\sqrt{\frac{\pi -1}{h+2\pi +4}}\text{, }h>-2\pi -4$$