Solve 5x^2+36=13x^2

$$5 x ^ { 2 } + 36 = 13 x ^ { 2 }$$

Solve for x

$$x = \frac{3 \sqrt{2}}{2} \approx 2.121320344$$

$$x = -\frac{3 \sqrt{2}}{2} \approx -2.121320344$$

Steps by Finding Square Root

Subtract 13x^{2} from both sides.

$$5x^{2}+36-13x^{2}=0$$

Combine 5x^{2} and -13x^{2} to get -8x^{2}.

$$-8x^{2}+36=0$$

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

$$-8x^{2}=-36$$

Divide both sides by -8.

$$x^{2}=\frac{-36}{-8}$$

Reduce the fraction \frac{-36}{-8} to lowest terms by extracting and canceling out -4.

$$x^{2}=\frac{9}{2}$$

Take the square root of both sides of the equation.

$$x=\frac{3\sqrt{2}}{2} x=-\frac{3\sqrt{2}}{2}$$

Steps Using the Quadratic Formula

Subtract 13x^{2} from both sides.

$$5x^{2}+36-13x^{2}=0$$

Combine 5x^{2} and -13x^{2} to get -8x^{2}.

$$-8x^{2}+36=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -8 for a, 0 for b, and 36 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-8\right)\times 36}}{2\left(-8\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-8\right)\times 36}}{2\left(-8\right)}$$

Multiply -4 times -8.

$$x=\frac{0±\sqrt{32\times 36}}{2\left(-8\right)}$$

Multiply 32 times 36.

$$x=\frac{0±\sqrt{1152}}{2\left(-8\right)}$$

Take the square root of 1152.

$$x=\frac{0±24\sqrt{2}}{2\left(-8\right)}$$

Multiply 2 times -8.

$$x=\frac{0±24\sqrt{2}}{-16}$$

Now solve the equation x=\frac{0±24\sqrt{2}}{-16} when ± is plus.

$$x=-\frac{3\sqrt{2}}{2}$$

Now solve the equation x=\frac{0±24\sqrt{2}}{-16} when ± is minus.

$$x=\frac{3\sqrt{2}}{2}$$

The equation is now solved.

$$x=-\frac{3\sqrt{2}}{2} x=\frac{3\sqrt{2}}{2}$$