Solve x1/2x=6

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

Solve for x

$$x=2\sqrt{3}\approx 3.464101615$$

$$x=-2\sqrt{3}\approx -3.464101615$$

Steps by Finding Square Root

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

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

Multiply both sides by 2, the reciprocal of \frac{1}{2}.

$$x^{2}=6\times 2$$

Multiply 6 and 2 to get 12.

$$x^{2}=12$$

Take the square root of both sides of the equation.

$$x=2\sqrt{3} x=-2\sqrt{3}$$

Steps Using the Quadratic Formula

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

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

Subtract 6 from both sides.

$$x^{2}\times \frac{1}{2}-6=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$\frac{1}{2}x^{2}-6=0$$

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

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

Square 0.

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

Multiply -4 times \frac{1}{2}.

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

Multiply -2 times -6.

$$x=\frac{0±\sqrt{12}}{2\times \frac{1}{2}}$$

Take the square root of 12.

$$x=\frac{0±2\sqrt{3}}{2\times \frac{1}{2}}$$

Multiply 2 times \frac{1}{2}.

$$x=\frac{0±2\sqrt{3}}{1}$$

Now solve the equation x=\frac{0±2\sqrt{3}}{1} when ± is plus.

$$x=2\sqrt{3}$$

Now solve the equation x=\frac{0±2\sqrt{3}}{1} when ± is minus.

$$x=-2\sqrt{3}$$

The equation is now solved.

$$x=2\sqrt{3} x=-2\sqrt{3}$$