Solve 16/h+4=h/2

$$\frac { 16 } { h + 4 } = \frac { h } { 2 }$$

Solve for h

$$h=-8$$

$$h=4$$

Steps Using the Quadratic Formula

Variable h cannot be equal to -4 since division by zero is not defined. Multiply both sides of the equation by 2\left(h+4\right), the least common multiple of h+4,2.

$$2\times 16=\left(h+4\right)h$$

Multiply 2 and 16 to get 32.

$$32=\left(h+4\right)h$$

Use the distributive property to multiply h+4 by h.

$$32=h^{2}+4h$$

Swap sides so that all variable terms are on the left hand side.

$$h^{2}+4h=32$$

Subtract 32 from both sides.

$$h^{2}+4h-32=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 4 for b, and -32 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$h=\frac{-4±\sqrt{4^{2}-4\left(-32\right)}}{2}$$

Square 4.

$$h=\frac{-4±\sqrt{16-4\left(-32\right)}}{2}$$

Multiply -4 times -32.

$$h=\frac{-4±\sqrt{16+128}}{2}$$

Add 16 to 128.

$$h=\frac{-4±\sqrt{144}}{2}$$

Take the square root of 144.

$$h=\frac{-4±12}{2}$$

Now solve the equation h=\frac{-4±12}{2} when ± is plus. Add -4 to 12.

$$h=\frac{8}{2}$$

Divide 8 by 2.

$$h=4$$

Now solve the equation h=\frac{-4±12}{2} when ± is minus. Subtract 12 from -4.

$$h=-\frac{16}{2}$$

Divide -16 by 2.

$$h=-8$$

The equation is now solved.

$$h=4 h=-8$$

Steps for Completing the Square

Variable h cannot be equal to -4 since division by zero is not defined. Multiply both sides of the equation by 2\left(h+4\right), the least common multiple of h+4,2.

$$2\times 16=\left(h+4\right)h$$

Multiply 2 and 16 to get 32.

$$32=\left(h+4\right)h$$

Use the distributive property to multiply h+4 by h.

$$32=h^{2}+4h$$

Swap sides so that all variable terms are on the left hand side.

$$h^{2}+4h=32$$

Divide 4, the coefficient of the x term, by 2 to get 2. Then add the square of 2 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$h^{2}+4h+2^{2}=32+2^{2}$$

Square 2.

$$h^{2}+4h+4=32+4$$

Add 32 to 4.

$$h^{2}+4h+4=36$$

Factor h^{2}+4h+4. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(h+2\right)^{2}=36$$

Take the square root of both sides of the equation.

$$\sqrt{\left(h+2\right)^{2}}=\sqrt{36}$$

Simplify.

$$h+2=6 h+2=-6$$

Subtract 2 from both sides of the equation.

$$h=4 h=-8$$