Solve 10x^2=254

$$10 x ^ { 2 } = 254$$

Solve for x

$$x = \frac{\sqrt{635}}{5} \approx 5.039841267$$

$$x = -\frac{\sqrt{635}}{5} \approx -5.039841267$$

Steps by Finding Square Root

Divide both sides by 10.

$$x^{2}=\frac{254}{10}$$

Reduce the fraction \frac{254}{10} to lowest terms by extracting and canceling out 2.

$$x^{2}=\frac{127}{5}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{635}}{5} x=-\frac{\sqrt{635}}{5}$$

Steps Using the Quadratic Formula

Divide both sides by 10.

$$x^{2}=\frac{254}{10}$$

Reduce the fraction \frac{254}{10} to lowest terms by extracting and canceling out 2.

$$x^{2}=\frac{127}{5}$$

Subtract \frac{127}{5} from both sides.

$$x^{2}-\frac{127}{5}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{127}{5} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{127}{5}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{127}{5}\right)}}{2}$$

Multiply -4 times -\frac{127}{5}.

$$x=\frac{0±\sqrt{\frac{508}{5}}}{2}$$

Take the square root of \frac{508}{5}.

$$x=\frac{0±\frac{2\sqrt{635}}{5}}{2}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{635}}{5}}{2} when ± is plus.

$$x=\frac{\sqrt{635}}{5}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{635}}{5}}{2} when ± is minus.

$$x=-\frac{\sqrt{635}}{5}$$

The equation is now solved.

$$x=\frac{\sqrt{635}}{5} x=-\frac{\sqrt{635}}{5}$$