Solve 45x^2=3

$$45 x ^ { 2 } = 3$$

Solve for x

$$x=\frac{\sqrt{15}}{15}\approx 0.25819889$$

$$x=-\frac{\sqrt{15}}{15}\approx -0.25819889$$

Steps by Finding Square Root

Divide both sides by 45.

$$x^{2}=\frac{3}{45}$$

Reduce the fraction \frac{3}{45} to lowest terms by extracting and canceling out 3.

$$x^{2}=\frac{1}{15}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{15}}{15} x=-\frac{\sqrt{15}}{15}$$

Steps Using the Quadratic Formula

Divide both sides by 45.

$$x^{2}=\frac{3}{45}$$

Reduce the fraction \frac{3}{45} to lowest terms by extracting and canceling out 3.

$$x^{2}=\frac{1}{15}$$

Subtract \frac{1}{15} from both sides.

$$x^{2}-\frac{1}{15}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{1}{15} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{1}{15}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{1}{15}\right)}}{2}$$

Multiply -4 times -\frac{1}{15}.

$$x=\frac{0±\sqrt{\frac{4}{15}}}{2}$$

Take the square root of \frac{4}{15}.

$$x=\frac{0±\frac{2\sqrt{15}}{15}}{2}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{15}}{15}}{2} when ± is plus.

$$x=\frac{\sqrt{15}}{15}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{15}}{15}}{2} when ± is minus.

$$x=-\frac{\sqrt{15}}{15}$$

The equation is now solved.

$$x=\frac{\sqrt{15}}{15} x=-\frac{\sqrt{15}}{15}$$