Solve 16/4-9/b^2=1

$$\frac { 16 } { 4 } - \frac { 9 } { b ^ { 2 } } = 1$$

Solve for b

$$b=\sqrt{3}\approx 1.732050808$$

$$b=-\sqrt{3}\approx -1.732050808$$

Steps by Finding Square Root

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4b^{2}, the least common multiple of 4,b^{2}.

$$b^{2}\times 16-4\times 9=4b^{2}$$

Multiply -4 and 9 to get -36.

$$b^{2}\times 16-36=4b^{2}$$

Subtract 4b^{2} from both sides.

$$b^{2}\times 16-36-4b^{2}=0$$

Combine b^{2}\times 16 and -4b^{2} to get 12b^{2}.

$$12b^{2}-36=0$$

Add 36 to both sides. Anything plus zero gives itself.

$$12b^{2}=36$$

Divide both sides by 12.

$$b^{2}=\frac{36}{12}$$

Divide 36 by 12 to get 3.

$$b^{2}=3$$

Take the square root of both sides of the equation.

$$b=\sqrt{3} b=-\sqrt{3}$$

Steps Using the Quadratic Formula

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4b^{2}, the least common multiple of 4,b^{2}.

$$b^{2}\times 16-4\times 9=4b^{2}$$

Multiply -4 and 9 to get -36.

$$b^{2}\times 16-36=4b^{2}$$

Subtract 4b^{2} from both sides.

$$b^{2}\times 16-36-4b^{2}=0$$

Combine b^{2}\times 16 and -4b^{2} to get 12b^{2}.

$$12b^{2}-36=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 12 for a, 0 for b, and -36 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\times 12\left(-36\right)}}{2\times 12}$$

Square 0.

$$b=\frac{0±\sqrt{-4\times 12\left(-36\right)}}{2\times 12}$$

Multiply -4 times 12.

$$b=\frac{0±\sqrt{-48\left(-36\right)}}{2\times 12}$$

Multiply -48 times -36.

$$b=\frac{0±\sqrt{1728}}{2\times 12}$$

Take the square root of 1728.

$$b=\frac{0±24\sqrt{3}}{2\times 12}$$

Multiply 2 times 12.

$$b=\frac{0±24\sqrt{3}}{24}$$

Now solve the equation b=\frac{0±24\sqrt{3}}{24} when ± is plus.

$$b=\sqrt{3}$$

Now solve the equation b=\frac{0±24\sqrt{3}}{24} when ± is minus.

$$b=-\sqrt{3}$$

The equation is now solved.

$$b=\sqrt{3} b=-\sqrt{3}$$