Solve x^2-13x^2+40=0

$${ x }^{ 2 } -13 { x }^{ 2 } +40=0$$

Solve for x

$$x = \frac{\sqrt{30}}{3} \approx 1.825741858$$

$$x = -\frac{\sqrt{30}}{3} \approx -1.825741858$$

Steps by Finding Square Root

Combine x^{2} and -13x^{2} to get -12x^{2}.

$$-12x^{2}+40=0$$

Subtract 40 from both sides. Anything subtracted from zero gives its negation.

$$-12x^{2}=-40$$

Divide both sides by -12.

$$x^{2}=\frac{-40}{-12}$$

Reduce the fraction \frac{-40}{-12} to lowest terms by extracting and canceling out -4.

$$x^{2}=\frac{10}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{30}}{3} x=-\frac{\sqrt{30}}{3}$$

Steps Using the Quadratic Formula

Combine x^{2} and -13x^{2} to get -12x^{2}.

$$-12x^{2}+40=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -12 for a, 0 for b, and 40 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-12\right)\times 40}}{2\left(-12\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-12\right)\times 40}}{2\left(-12\right)}$$

Multiply -4 times -12.

$$x=\frac{0±\sqrt{48\times 40}}{2\left(-12\right)}$$

Multiply 48 times 40.

$$x=\frac{0±\sqrt{1920}}{2\left(-12\right)}$$

Take the square root of 1920.

$$x=\frac{0±8\sqrt{30}}{2\left(-12\right)}$$

Multiply 2 times -12.

$$x=\frac{0±8\sqrt{30}}{-24}$$

Now solve the equation x=\frac{0±8\sqrt{30}}{-24} when ± is plus.

$$x=-\frac{\sqrt{30}}{3}$$

Now solve the equation x=\frac{0±8\sqrt{30}}{-24} when ± is minus.

$$x=\frac{\sqrt{30}}{3}$$

The equation is now solved.

$$x=-\frac{\sqrt{30}}{3} x=\frac{\sqrt{30}}{3}$$