Solve (6sqrt{13})^2=12^2+x^2

$$( 6 \sqrt { 13 } ) ^ { 2 } = 12 ^ { 2 } + x ^ { 2 }$$

Solve for x

$$x=18$$

$$x=-18$$

Steps Using Difference of Squares

Expand \left(6\sqrt{13}\right)^{2}.

$$6^{2}\left(\sqrt{13}\right)^{2}=12^{2}+x^{2}$$

Calculate 6 to the power of 2 and get 36.

$$36\left(\sqrt{13}\right)^{2}=12^{2}+x^{2}$$

The square of \sqrt{13} is 13.

$$36\times 13=12^{2}+x^{2}$$

Multiply 36 and 13 to get 468.

$$468=12^{2}+x^{2}$$

Calculate 12 to the power of 2 and get 144.

$$468=144+x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$144+x^{2}=468$$

Subtract 468 from both sides.

$$144+x^{2}-468=0$$

Subtract 468 from 144 to get -324.

$$-324+x^{2}=0$$

Consider -324+x^{2}. Rewrite -324+x^{2} as x^{2}-18^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-18\right)\left(x+18\right)=0$$

To find equation solutions, solve x-18=0 and x+18=0.

$$x=18 x=-18$$

Steps by Finding Square Root

Expand \left(6\sqrt{13}\right)^{2}.

$$6^{2}\left(\sqrt{13}\right)^{2}=12^{2}+x^{2}$$

Calculate 6 to the power of 2 and get 36.

$$36\left(\sqrt{13}\right)^{2}=12^{2}+x^{2}$$

The square of \sqrt{13} is 13.

$$36\times 13=12^{2}+x^{2}$$

Multiply 36 and 13 to get 468.

$$468=12^{2}+x^{2}$$

Calculate 12 to the power of 2 and get 144.

$$468=144+x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$144+x^{2}=468$$

Subtract 144 from both sides.

$$x^{2}=468-144$$

Subtract 144 from 468 to get 324.

$$x^{2}=324$$

Take the square root of both sides of the equation.

$$x=18 x=-18$$

Steps Using the Quadratic Formula

Expand \left(6\sqrt{13}\right)^{2}.

$$6^{2}\left(\sqrt{13}\right)^{2}=12^{2}+x^{2}$$

Calculate 6 to the power of 2 and get 36.

$$36\left(\sqrt{13}\right)^{2}=12^{2}+x^{2}$$

The square of \sqrt{13} is 13.

$$36\times 13=12^{2}+x^{2}$$

Multiply 36 and 13 to get 468.

$$468=12^{2}+x^{2}$$

Calculate 12 to the power of 2 and get 144.

$$468=144+x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$144+x^{2}=468$$

Subtract 468 from both sides.

$$144+x^{2}-468=0$$

Subtract 468 from 144 to get -324.

$$-324+x^{2}=0$$

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.

$$x^{2}-324=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -324 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-324\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-324\right)}}{2}$$

Multiply -4 times -324.

$$x=\frac{0±\sqrt{1296}}{2}$$

Take the square root of 1296.

$$x=\frac{0±36}{2}$$

Now solve the equation x=\frac{0±36}{2} when ± is plus. Divide 36 by 2.

$$x=18$$

Now solve the equation x=\frac{0±36}{2} when ± is minus. Divide -36 by 2.

$$x=-18$$

The equation is now solved.

$$x=18 x=-18$$