Solve 1/4+3/2b^2=1

$$\frac { 1 } { 4 } + \frac { 3 } { 2 b ^ { 2 } } = 1$$

Solve for b

$$b=\sqrt{2}\approx 1.414213562$$

$$b=-\sqrt{2}\approx -1.414213562$$

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 4,2b^{2}.

$$4b^{2}\times \frac{1}{4}+2\times 3=4b^{2}$$

Multiply 4 and \frac{1}{4} to get 1.

$$b^{2}+2\times 3=4b^{2}$$

Multiply 2 and 3 to get 6.

$$b^{2}+6=4b^{2}$$

Subtract 4b^{2} from both sides.

$$b^{2}+6-4b^{2}=0$$

Combine b^{2} and -4b^{2} to get -3b^{2}.

$$-3b^{2}+6=0$$

Subtract 6 from both sides. Anything subtracted from zero gives its negation.

$$-3b^{2}=-6$$

Divide both sides by -3.

$$b^{2}=\frac{-6}{-3}$$

Divide -6 by -3 to get 2.

$$b^{2}=2$$

Take the square root of both sides of the equation.

$$b=\sqrt{2} b=-\sqrt{2}$$

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 4,2b^{2}.

$$4b^{2}\times \frac{1}{4}+2\times 3=4b^{2}$$

Multiply 4 and \frac{1}{4} to get 1.

$$b^{2}+2\times 3=4b^{2}$$

Multiply 2 and 3 to get 6.

$$b^{2}+6=4b^{2}$$

Subtract 4b^{2} from both sides.

$$b^{2}+6-4b^{2}=0$$

Combine b^{2} and -4b^{2} to get -3b^{2}.

$$-3b^{2}+6=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -3 for a, 0 for b, and 6 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\left(-3\right)\times 6}}{2\left(-3\right)}$$

Square 0.

$$b=\frac{0±\sqrt{-4\left(-3\right)\times 6}}{2\left(-3\right)}$$

Multiply -4 times -3.

$$b=\frac{0±\sqrt{12\times 6}}{2\left(-3\right)}$$

Multiply 12 times 6.

$$b=\frac{0±\sqrt{72}}{2\left(-3\right)}$$

Take the square root of 72.

$$b=\frac{0±6\sqrt{2}}{2\left(-3\right)}$$

Multiply 2 times -3.

$$b=\frac{0±6\sqrt{2}}{-6}$$

Now solve the equation b=\frac{0±6\sqrt{2}}{-6} when ± is plus.

$$b=-\sqrt{2}$$

Now solve the equation b=\frac{0±6\sqrt{2}}{-6} when ± is minus.

$$b=\sqrt{2}$$

The equation is now solved.

$$b=-\sqrt{2} b=\sqrt{2}$$