Solve 4/a=a/16

$$\frac { 4 } { a } = \frac { a } { 16 }$$

Solve for a

$$a=8$$

$$a=-8$$

Steps by Finding Square Root

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 16a, the least common multiple of a,16.

$$16\times 4=aa$$

Multiply a and a to get a^{2}.

$$16\times 4=a^{2}$$

Multiply 16 and 4 to get 64.

$$64=a^{2}$$

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

$$a^{2}=64$$

Take the square root of both sides of the equation.

$$a=8 a=-8$$

Steps Using the Quadratic Formula

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 16a, the least common multiple of a,16.

$$16\times 4=aa$$

Multiply a and a to get a^{2}.

$$16\times 4=a^{2}$$

Multiply 16 and 4 to get 64.

$$64=a^{2}$$

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

$$a^{2}=64$$

Subtract 64 from both sides.

$$a^{2}-64=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -64 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\left(-64\right)}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\left(-64\right)}}{2}$$

Multiply -4 times -64.

$$a=\frac{0±\sqrt{256}}{2}$$

Take the square root of 256.

$$a=\frac{0±16}{2}$$

Now solve the equation a=\frac{0±16}{2} when ± is plus. Divide 16 by 2.

$$a=8$$

Now solve the equation a=\frac{0±16}{2} when ± is minus. Divide -16 by 2.

$$a=-8$$

The equation is now solved.

$$a=8 a=-8$$