Solve 6^2+6^2=x^2

$${ 6 }^{ 2 } + { 6 }^{ 2 } = { x }^{ 2 }$$

Solve for x

$$x=6\sqrt{2}\approx 8.485281374$$

$$x=-6\sqrt{2}\approx -8.485281374$$

Steps by Finding Square Root

Calculate 6 to the power of 2 and get 36.

$$36+6^{2}=x^{2}$$

Calculate 6 to the power of 2 and get 36.

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

Add 36 and 36 to get 72.

$$72=x^{2}$$

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

$$x^{2}=72$$

Take the square root of both sides of the equation.

$$x=6\sqrt{2} x=-6\sqrt{2}$$

Steps Using the Quadratic Formula

Calculate 6 to the power of 2 and get 36.

$$36+6^{2}=x^{2}$$

Calculate 6 to the power of 2 and get 36.

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

Add 36 and 36 to get 72.

$$72=x^{2}$$

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

$$x^{2}=72$$

Subtract 72 from both sides.

$$x^{2}-72=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -72 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-72\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-72\right)}}{2}$$

Multiply -4 times -72.

$$x=\frac{0±\sqrt{288}}{2}$$

Take the square root of 288.

$$x=\frac{0±12\sqrt{2}}{2}$$

Now solve the equation x=\frac{0±12\sqrt{2}}{2} when ± is plus.

$$x=6\sqrt{2}$$

Now solve the equation x=\frac{0±12\sqrt{2}}{2} when ± is minus.

$$x=-6\sqrt{2}$$

The equation is now solved.

$$x=6\sqrt{2} x=-6\sqrt{2}$$