Solve 2/5x^2=9

$$\frac { 2 } { 5 } x ^ { 2 } = 9$$

Solve for x

$$x = \frac{3 \sqrt{10}}{2} \approx 4.74341649$$

$$x = -\frac{3 \sqrt{10}}{2} \approx -4.74341649$$

Steps by Finding Square Root

Multiply both sides by \frac{5}{2}, the reciprocal of \frac{2}{5}.

$$x^{2}=9\times \frac{5}{2}$$

Multiply 9 and \frac{5}{2} to get \frac{45}{2}.

$$x^{2}=\frac{45}{2}$$

Take the square root of both sides of the equation.

$$x=\frac{3\sqrt{10}}{2} x=-\frac{3\sqrt{10}}{2}$$

Steps Using the Quadratic Formula

Multiply both sides by \frac{5}{2}, the reciprocal of \frac{2}{5}.

$$x^{2}=9\times \frac{5}{2}$$

Multiply 9 and \frac{5}{2} to get \frac{45}{2}.

$$x^{2}=\frac{45}{2}$$

Subtract \frac{45}{2} from both sides.

$$x^{2}-\frac{45}{2}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{45}{2} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{45}{2}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{45}{2}\right)}}{2}$$

Multiply -4 times -\frac{45}{2}.

$$x=\frac{0±\sqrt{90}}{2}$$

Take the square root of 90.

$$x=\frac{0±3\sqrt{10}}{2}$$

Now solve the equation x=\frac{0±3\sqrt{10}}{2} when ± is plus.

$$x=\frac{3\sqrt{10}}{2}$$

Now solve the equation x=\frac{0±3\sqrt{10}}{2} when ± is minus.

$$x=-\frac{3\sqrt{10}}{2}$$

The equation is now solved.

$$x=\frac{3\sqrt{10}}{2} x=-\frac{3\sqrt{10}}{2}$$