Solve 10-2x^2=0

$$10 - 2 x ^ { 2 } = 0$$

Solve for x

$$x=\sqrt{5}\approx 2.236067977$$

$$x=-\sqrt{5}\approx -2.236067977$$

Steps by Finding Square Root

Subtract 10 from both sides. Anything subtracted from zero gives its negation.

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

Divide both sides by -2.

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

Divide -10 by -2 to get 5.

$$x^{2}=5$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-2x^{2}+10=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -2 for a, 0 for b, and 10 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-2\right)\times 10}}{2\left(-2\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-2\right)\times 10}}{2\left(-2\right)}$$

Multiply -4 times -2.

$$x=\frac{0±\sqrt{8\times 10}}{2\left(-2\right)}$$

Multiply 8 times 10.

$$x=\frac{0±\sqrt{80}}{2\left(-2\right)}$$

Take the square root of 80.

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

Multiply 2 times -2.

$$x=\frac{0±4\sqrt{5}}{-4}$$

Now solve the equation x=\frac{0±4\sqrt{5}}{-4} when ± is plus.

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

Now solve the equation x=\frac{0±4\sqrt{5}}{-4} when ± is minus.

$$x=\sqrt{5}$$

The equation is now solved.

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