Solve left(5xright)^2+36=left(13xright)^2

$${ \left(5x \right) }^{ 2 } +36= { \left(13x \right) }^{ 2 }$$

Solve for x

$$x=\frac{1}{2}=0.5$$

$$x=-\frac{1}{2}=-0.5$$

Steps by Finding Square Root

Expand \left(5x\right)^{2}.

$$5^{2}x^{2}+36=\left(13x\right)^{2}$$

Calculate 5 to the power of 2 and get 25.

$$25x^{2}+36=\left(13x\right)^{2}$$

Expand \left(13x\right)^{2}.

$$25x^{2}+36=13^{2}x^{2}$$

Calculate 13 to the power of 2 and get 169.

$$25x^{2}+36=169x^{2}$$

Subtract 169x^{2} from both sides.

$$25x^{2}+36-169x^{2}=0$$

Combine 25x^{2} and -169x^{2} to get -144x^{2}.

$$-144x^{2}+36=0$$

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

$$-144x^{2}=-36$$

Divide both sides by -144.

$$x^{2}=\frac{-36}{-144}$$

Reduce the fraction \frac{-36}{-144} to lowest terms by extracting and canceling out -36.

$$x^{2}=\frac{1}{4}$$

Take the square root of both sides of the equation.

$$x=\frac{1}{2} x=-\frac{1}{2}$$

Steps Using the Quadratic Formula

Expand \left(5x\right)^{2}.

$$5^{2}x^{2}+36=\left(13x\right)^{2}$$

Calculate 5 to the power of 2 and get 25.

$$25x^{2}+36=\left(13x\right)^{2}$$

Expand \left(13x\right)^{2}.

$$25x^{2}+36=13^{2}x^{2}$$

Calculate 13 to the power of 2 and get 169.

$$25x^{2}+36=169x^{2}$$

Subtract 169x^{2} from both sides.

$$25x^{2}+36-169x^{2}=0$$

Combine 25x^{2} and -169x^{2} to get -144x^{2}.

$$-144x^{2}+36=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -144 for a, 0 for b, and 36 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-144\right)\times 36}}{2\left(-144\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-144\right)\times 36}}{2\left(-144\right)}$$

Multiply -4 times -144.

$$x=\frac{0±\sqrt{576\times 36}}{2\left(-144\right)}$$

Multiply 576 times 36.

$$x=\frac{0±\sqrt{20736}}{2\left(-144\right)}$$

Take the square root of 20736.

$$x=\frac{0±144}{2\left(-144\right)}$$

Multiply 2 times -144.

$$x=\frac{0±144}{-288}$$

Now solve the equation x=\frac{0±144}{-288} when ± is plus. Reduce the fraction \frac{144}{-288} to lowest terms by extracting and canceling out 144.

$$x=-\frac{1}{2}$$

Now solve the equation x=\frac{0±144}{-288} when ± is minus. Reduce the fraction \frac{-144}{-288} to lowest terms by extracting and canceling out 144.

$$x=\frac{1}{2}$$

The equation is now solved.

$$x=-\frac{1}{2} x=\frac{1}{2}$$