Solve (1/2(x)(x))(9)=12

$$( \frac { 1 } { 2 } ( x ) ( x ) ) ( 9 ) = 12$$

Solve for x

$$x = \frac{2 \sqrt{6}}{3} \approx 1.632993162$$

$$x = -\frac{2 \sqrt{6}}{3} \approx -1.632993162$$

Steps by Finding Square Root

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

$$\frac{1}{2}x^{2}\times 9=12$$

Multiply \frac{1}{2} and 9 to get \frac{9}{2}.

$$\frac{9}{2}x^{2}=12$$

Multiply both sides by \frac{2}{9}, the reciprocal of \frac{9}{2}.

$$x^{2}=12\times \frac{2}{9}$$

Express 12\times \frac{2}{9} as a single fraction.

$$x^{2}=\frac{12\times 2}{9}$$

Multiply 12 and 2 to get 24.

$$x^{2}=\frac{24}{9}$$

Reduce the fraction \frac{24}{9} to lowest terms by extracting and canceling out 3.

$$x^{2}=\frac{8}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{2\sqrt{6}}{3} x=-\frac{2\sqrt{6}}{3}$$

Steps Using the Quadratic Formula

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

$$\frac{1}{2}x^{2}\times 9=12$$

Multiply \frac{1}{2} and 9 to get \frac{9}{2}.

$$\frac{9}{2}x^{2}=12$$

Subtract 12 from both sides.

$$\frac{9}{2}x^{2}-12=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{9}{2} for a, 0 for b, and -12 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{9}{2}\left(-12\right)}}{2\times \frac{9}{2}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{9}{2}\left(-12\right)}}{2\times \frac{9}{2}}$$

Multiply -4 times \frac{9}{2}.

$$x=\frac{0±\sqrt{-18\left(-12\right)}}{2\times \frac{9}{2}}$$

Multiply -18 times -12.

$$x=\frac{0±\sqrt{216}}{2\times \frac{9}{2}}$$

Take the square root of 216.

$$x=\frac{0±6\sqrt{6}}{2\times \frac{9}{2}}$$

Multiply 2 times \frac{9}{2}.

$$x=\frac{0±6\sqrt{6}}{9}$$

Now solve the equation x=\frac{0±6\sqrt{6}}{9} when ± is plus.

$$x=\frac{2\sqrt{6}}{3}$$

Now solve the equation x=\frac{0±6\sqrt{6}}{9} when ± is minus.

$$x=-\frac{2\sqrt{6}}{3}$$

The equation is now solved.

$$x=\frac{2\sqrt{6}}{3} x=-\frac{2\sqrt{6}}{3}$$