Solve h^2+6^2=(6sqrt{2})^2

$$h ^ { 2 } + 6 ^ { 2 } = ( 6 \sqrt { 2 } ) ^ { 2 }$$

Solve for h

$$h=-6$$

$$h=6$$

Steps Using Difference of Squares

Calculate 6 to the power of 2 and get 36.

$$h^{2}+36=\left(6\sqrt{2}\right)^{2}$$

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

$$h^{2}+36=6^{2}\left(\sqrt{2}\right)^{2}$$

Calculate 6 to the power of 2 and get 36.

$$h^{2}+36=36\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$h^{2}+36=36\times 2$$

Multiply 36 and 2 to get 72.

$$h^{2}+36=72$$

Subtract 72 from both sides.

$$h^{2}+36-72=0$$

Subtract 72 from 36 to get -36.

$$h^{2}-36=0$$

Consider h^{2}-36. Rewrite h^{2}-36 as h^{2}-6^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(h-6\right)\left(h+6\right)=0$$

To find equation solutions, solve h-6=0 and h+6=0.

$$h=6 h=-6$$

Steps by Finding Square Root

Calculate 6 to the power of 2 and get 36.

$$h^{2}+36=\left(6\sqrt{2}\right)^{2}$$

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

$$h^{2}+36=6^{2}\left(\sqrt{2}\right)^{2}$$

Calculate 6 to the power of 2 and get 36.

$$h^{2}+36=36\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$h^{2}+36=36\times 2$$

Multiply 36 and 2 to get 72.

$$h^{2}+36=72$$

Subtract 36 from both sides.

$$h^{2}=72-36$$

Subtract 36 from 72 to get 36.

$$h^{2}=36$$

Take the square root of both sides of the equation.

$$h=6 h=-6$$

Steps Using the Quadratic Formula

Calculate 6 to the power of 2 and get 36.

$$h^{2}+36=\left(6\sqrt{2}\right)^{2}$$

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

$$h^{2}+36=6^{2}\left(\sqrt{2}\right)^{2}$$

Calculate 6 to the power of 2 and get 36.

$$h^{2}+36=36\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$h^{2}+36=36\times 2$$

Multiply 36 and 2 to get 72.

$$h^{2}+36=72$$

Subtract 72 from both sides.

$$h^{2}+36-72=0$$

Subtract 72 from 36 to get -36.

$$h^{2}-36=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -36 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Square 0.

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

Multiply -4 times -36.

$$h=\frac{0±\sqrt{144}}{2}$$

Take the square root of 144.

$$h=\frac{0±12}{2}$$

Now solve the equation h=\frac{0±12}{2} when ± is plus. Divide 12 by 2.

$$h=6$$

Now solve the equation h=\frac{0±12}{2} when ± is minus. Divide -12 by 2.

$$h=-6$$

The equation is now solved.

$$h=6 h=-6$$