Solve x^2=9^2+6^2

$${ x }^{ 2 } = { 9 }^{ 2 } + { 6 }^{ 2 }$$

Solve for x

$$x=3\sqrt{13}\approx 10.816653826$$

$$x=-3\sqrt{13}\approx -10.816653826$$

Steps by Finding Square Root

Calculate 9 to the power of 2 and get 81.

$$x^{2}=81+6^{2}$$

Calculate 6 to the power of 2 and get 36.

$$x^{2}=81+36$$

Add 81 and 36 to get 117.

$$x^{2}=117$$

Take the square root of both sides of the equation.

$$x=3\sqrt{13} x=-3\sqrt{13}$$

Steps Using the Quadratic Formula

Calculate 9 to the power of 2 and get 81.

$$x^{2}=81+6^{2}$$

Calculate 6 to the power of 2 and get 36.

$$x^{2}=81+36$$

Add 81 and 36 to get 117.

$$x^{2}=117$$

Subtract 117 from both sides.

$$x^{2}-117=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -117 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-117\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-117\right)}}{2}$$

Multiply -4 times -117.

$$x=\frac{0±\sqrt{468}}{2}$$

Take the square root of 468.

$$x=\frac{0±6\sqrt{13}}{2}$$

Now solve the equation x=\frac{0±6\sqrt{13}}{2} when ± is plus.

$$x=3\sqrt{13}$$

Now solve the equation x=\frac{0±6\sqrt{13}}{2} when ± is minus.

$$x=-3\sqrt{13}$$

The equation is now solved.

$$x=3\sqrt{13} x=-3\sqrt{13}$$