Solve 152.5=5x^2

$$152.5 = 5 x ^ { 2 }$$

Solve for x

$$x = \frac{\sqrt{122}}{2} \approx 5.522680509$$

$$x = -\frac{\sqrt{122}}{2} \approx -5.522680509$$

Steps by Finding Square Root

Divide both sides by 5.

$$\frac{152.5}{5}=x^{2}$$

Expand \frac{152.5}{5} by multiplying both numerator and the denominator by 10.

$$\frac{1525}{50}=x^{2}$$

Reduce the fraction \frac{1525}{50} to lowest terms by extracting and canceling out 25.

$$\frac{61}{2}=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=\frac{61}{2}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{122}}{2} x=-\frac{\sqrt{122}}{2}$$

Steps Using the Quadratic Formula

Divide both sides by 5.

$$\frac{152.5}{5}=x^{2}$$

Expand \frac{152.5}{5} by multiplying both numerator and the denominator by 10.

$$\frac{1525}{50}=x^{2}$$

Reduce the fraction \frac{1525}{50} to lowest terms by extracting and canceling out 25.

$$\frac{61}{2}=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=\frac{61}{2}$$

Subtract \frac{61}{2} from both sides.

$$x^{2}-\frac{61}{2}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{61}{2} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{61}{2}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{61}{2}\right)}}{2}$$

Multiply -4 times -\frac{61}{2}.

$$x=\frac{0±\sqrt{122}}{2}$$

Now solve the equation x=\frac{0±\sqrt{122}}{2} when ± is plus.

$$x=\frac{\sqrt{122}}{2}$$

Now solve the equation x=\frac{0±\sqrt{122}}{2} when ± is minus.

$$x=-\frac{\sqrt{122}}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{122}}{2} x=-\frac{\sqrt{122}}{2}$$