Solve 1/2x^2*3^2=7

$$\frac { 1 } { 2 } x ^ { 2 } \times 3 ^ { 2 } = 7$$

Solve for x

$$x = \frac{\sqrt{14}}{3} \approx 1.247219129$$

$$x = -\frac{\sqrt{14}}{3} \approx -1.247219129$$

Steps by Finding Square Root

Calculate 3 to the power of 2 and get 9.

$$\frac{1}{2}x^{2}\times 9=7$$

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

$$\frac{9}{2}x^{2}=7$$

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

$$x^{2}=7\times \frac{2}{9}$$

Multiply 7 and \frac{2}{9} to get \frac{14}{9}.

$$x^{2}=\frac{14}{9}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{14}}{3} x=-\frac{\sqrt{14}}{3}$$

Steps Using the Quadratic Formula

Calculate 3 to the power of 2 and get 9.

$$\frac{1}{2}x^{2}\times 9=7$$

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

$$\frac{9}{2}x^{2}=7$$

Subtract 7 from both sides.

$$\frac{9}{2}x^{2}-7=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{9}{2} for a, 0 for b, and -7 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{9}{2}\left(-7\right)}}{2\times \frac{9}{2}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{9}{2}\left(-7\right)}}{2\times \frac{9}{2}}$$

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

$$x=\frac{0±\sqrt{-18\left(-7\right)}}{2\times \frac{9}{2}}$$

Multiply -18 times -7.

$$x=\frac{0±\sqrt{126}}{2\times \frac{9}{2}}$$

Take the square root of 126.

$$x=\frac{0±3\sqrt{14}}{2\times \frac{9}{2}}$$

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

$$x=\frac{0±3\sqrt{14}}{9}$$

Now solve the equation x=\frac{0±3\sqrt{14}}{9} when ± is plus.

$$x=\frac{\sqrt{14}}{3}$$

Now solve the equation x=\frac{0±3\sqrt{14}}{9} when ± is minus.

$$x=-\frac{\sqrt{14}}{3}$$

The equation is now solved.

$$x=\frac{\sqrt{14}}{3} x=-\frac{\sqrt{14}}{3}$$