Solve -13x^2+11=0

$$- 13 x ^ { 2 } + 11 = 0$$

Solve for x

$$x=\frac{\sqrt{143}}{13}\approx 0.919866211$$

$$x=-\frac{\sqrt{143}}{13}\approx -0.919866211$$

Steps by Finding Square Root

Subtract 11 from both sides. Anything subtracted from zero gives its negation.

$$-13x^{2}=-11$$

Divide both sides by -13.

$$x^{2}=\frac{-11}{-13}$$

Fraction \frac{-11}{-13} can be simplified to \frac{11}{13} by removing the negative sign from both the numerator and the denominator.

$$x^{2}=\frac{11}{13}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{143}}{13} x=-\frac{\sqrt{143}}{13}$$

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.

$$-13x^{2}+11=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -13 for a, 0 for b, and 11 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-13\right)\times 11}}{2\left(-13\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-13\right)\times 11}}{2\left(-13\right)}$$

Multiply -4 times -13.

$$x=\frac{0±\sqrt{52\times 11}}{2\left(-13\right)}$$

Multiply 52 times 11.

$$x=\frac{0±\sqrt{572}}{2\left(-13\right)}$$

Take the square root of 572.

$$x=\frac{0±2\sqrt{143}}{2\left(-13\right)}$$

Multiply 2 times -13.

$$x=\frac{0±2\sqrt{143}}{-26}$$

Now solve the equation x=\frac{0±2\sqrt{143}}{-26} when ± is plus.

$$x=-\frac{\sqrt{143}}{13}$$

Now solve the equation x=\frac{0±2\sqrt{143}}{-26} when ± is minus.

$$x=\frac{\sqrt{143}}{13}$$

The equation is now solved.

$$x=-\frac{\sqrt{143}}{13} x=\frac{\sqrt{143}}{13}$$