Solve 16/a^2-15/9a^2=1

$$\frac { 16 } { a ^ { 2 } } - \frac { 15 } { 9 a ^ { 2 } } = 1$$

Solve for a

$$a = \frac{\sqrt{129}}{3} \approx 3.785938897$$

$$a = -\frac{\sqrt{129}}{3} \approx -3.785938897$$

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 9a^{2}, the least common multiple of a^{2},9a^{2}.

$$9\times 16-15=9a^{2}$$

Multiply 9 and 16 to get 144.

$$144-15=9a^{2}$$

Subtract 15 from 144 to get 129.

$$129=9a^{2}$$

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

$$9a^{2}=129$$

Divide both sides by 9.

$$a^{2}=\frac{129}{9}$$

Reduce the fraction \frac{129}{9} to lowest terms by extracting and canceling out 3.

$$a^{2}=\frac{43}{3}$$

Take the square root of both sides of the equation.

$$a=\frac{\sqrt{129}}{3} a=-\frac{\sqrt{129}}{3}$$

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 9a^{2}, the least common multiple of a^{2},9a^{2}.

$$9\times 16-15=9a^{2}$$

Multiply 9 and 16 to get 144.

$$144-15=9a^{2}$$

Subtract 15 from 144 to get 129.

$$129=9a^{2}$$

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

$$9a^{2}=129$$

Subtract 129 from both sides.

$$9a^{2}-129=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 9 for a, 0 for b, and -129 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\times 9\left(-129\right)}}{2\times 9}$$

Square 0.

$$a=\frac{0±\sqrt{-4\times 9\left(-129\right)}}{2\times 9}$$

Multiply -4 times 9.

$$a=\frac{0±\sqrt{-36\left(-129\right)}}{2\times 9}$$

Multiply -36 times -129.

$$a=\frac{0±\sqrt{4644}}{2\times 9}$$

Take the square root of 4644.

$$a=\frac{0±6\sqrt{129}}{2\times 9}$$

Multiply 2 times 9.

$$a=\frac{0±6\sqrt{129}}{18}$$

Now solve the equation a=\frac{0±6\sqrt{129}}{18} when ± is plus.

$$a=\frac{\sqrt{129}}{3}$$

Now solve the equation a=\frac{0±6\sqrt{129}}{18} when ± is minus.

$$a=-\frac{\sqrt{129}}{3}$$

The equation is now solved.

$$a=\frac{\sqrt{129}}{3} a=-\frac{\sqrt{129}}{3}$$