Solve -5x^2+13=0

$$-5 { x }^{ 2 } +13 = 0$$

Solve for x

$$x = \frac{\sqrt{65}}{5} \approx 1.61245155$$

$$x = -\frac{\sqrt{65}}{5} \approx -1.61245155$$

Steps by Finding Square Root

Subtract 13 from both sides. Anything subtracted from zero gives its negation.

$$-5x^{2}=-13$$

Divide both sides by -5.

$$x^{2}=\frac{-13}{-5}$$

Fraction \frac{-13}{-5} can be simplified to \frac{13}{5} by removing the negative sign from both the numerator and the denominator.

$$x^{2}=\frac{13}{5}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{65}}{5} x=-\frac{\sqrt{65}}{5}$$

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.

$$-5x^{2}+13=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -5 for a, 0 for b, and 13 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-5\right)\times 13}}{2\left(-5\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-5\right)\times 13}}{2\left(-5\right)}$$

Multiply -4 times -5.

$$x=\frac{0±\sqrt{20\times 13}}{2\left(-5\right)}$$

Multiply 20 times 13.

$$x=\frac{0±\sqrt{260}}{2\left(-5\right)}$$

Take the square root of 260.

$$x=\frac{0±2\sqrt{65}}{2\left(-5\right)}$$

Multiply 2 times -5.

$$x=\frac{0±2\sqrt{65}}{-10}$$

Now solve the equation x=\frac{0±2\sqrt{65}}{-10} when ± is plus.

$$x=-\frac{\sqrt{65}}{5}$$

Now solve the equation x=\frac{0±2\sqrt{65}}{-10} when ± is minus.

$$x=\frac{\sqrt{65}}{5}$$

The equation is now solved.

$$x=-\frac{\sqrt{65}}{5} x=\frac{\sqrt{65}}{5}$$