Solve 1/2+3/x^2=1

$$\frac { 1 } { 2 } + \frac { 3 } { x ^ { 2 } } = 1$$

Solve for x

$$x=\sqrt{6}\approx 2.449489743$$

$$x=-\sqrt{6}\approx -2.449489743$$

Steps by Finding Square Root

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

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

Multiply 2 and \frac{1}{2} to get 1.

$$x^{2}+2\times 3=2x^{2}$$

Multiply 2 and 3 to get 6.

$$x^{2}+6=2x^{2}$$

Subtract 2x^{2} from both sides.

$$x^{2}+6-2x^{2}=0$$

Combine x^{2} and -2x^{2} to get -x^{2}.

$$-x^{2}+6=0$$

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

$$-x^{2}=-6$$

Divide both sides by -1.

$$x^{2}=\frac{-6}{-1}$$

Fraction \frac{-6}{-1} can be simplified to 6 by removing the negative sign from both the numerator and the denominator.

$$x^{2}=6$$

Take the square root of both sides of the equation.

$$x=\sqrt{6} x=-\sqrt{6}$$

Steps Using the Quadratic Formula

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

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

Multiply 2 and \frac{1}{2} to get 1.

$$x^{2}+2\times 3=2x^{2}$$

Multiply 2 and 3 to get 6.

$$x^{2}+6=2x^{2}$$

Subtract 2x^{2} from both sides.

$$x^{2}+6-2x^{2}=0$$

Combine x^{2} and -2x^{2} to get -x^{2}.

$$-x^{2}+6=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 6 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 6}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 6}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\times 6}}{2\left(-1\right)}$$

Multiply 4 times 6.

$$x=\frac{0±\sqrt{24}}{2\left(-1\right)}$$

Take the square root of 24.

$$x=\frac{0±2\sqrt{6}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±2\sqrt{6}}{-2}$$

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

$$x=-\sqrt{6}$$

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

$$x=\sqrt{6}$$

The equation is now solved.

$$x=-\sqrt{6} x=\sqrt{6}$$