Solve x^2-13x^2+36=0

$$x ^ { 2 } - 13 x ^ { 2 } + 36 = 0$$

Solve for x

$$x=\sqrt{3}\approx 1.732050808$$

$$x=-\sqrt{3}\approx -1.732050808$$

Steps by Finding Square Root

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

$$-12x^{2}+36=0$$

Subtract 36 from both sides. Anything subtracted from zero gives its negation.

$$-12x^{2}=-36$$

Divide both sides by -12.

$$x^{2}=\frac{-36}{-12}$$

Divide -36 by -12 to get 3.

$$x^{2}=3$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

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

$$-12x^{2}+36=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -12 for a, 0 for b, and 36 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-12\right)\times 36}}{2\left(-12\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-12\right)\times 36}}{2\left(-12\right)}$$

Multiply -4 times -12.

$$x=\frac{0±\sqrt{48\times 36}}{2\left(-12\right)}$$

Multiply 48 times 36.

$$x=\frac{0±\sqrt{1728}}{2\left(-12\right)}$$

Take the square root of 1728.

$$x=\frac{0±24\sqrt{3}}{2\left(-12\right)}$$

Multiply 2 times -12.

$$x=\frac{0±24\sqrt{3}}{-24}$$

Now solve the equation x=\frac{0±24\sqrt{3}}{-24} when ± is plus.

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

Now solve the equation x=\frac{0±24\sqrt{3}}{-24} when ± is minus.

$$x=\sqrt{3}$$

The equation is now solved.

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