Solve x^2+8^2=9^2

$$x ^ { 2 } + 8 ^ { 2 } = 9 ^ { 2 }$$

Solve for x

$$x=\sqrt{17}\approx 4.123105626$$

$$x=-\sqrt{17}\approx -4.123105626$$

Steps by Finding Square Root

Calculate 8 to the power of 2 and get 64.

$$x^{2}+64=9^{2}$$

Calculate 9 to the power of 2 and get 81.

$$x^{2}+64=81$$

Subtract 64 from both sides.

$$x^{2}=81-64$$

Subtract 64 from 81 to get 17.

$$x^{2}=17$$

Take the square root of both sides of the equation.

$$x=\sqrt{17} x=-\sqrt{17}$$

Steps Using the Quadratic Formula

Calculate 8 to the power of 2 and get 64.

$$x^{2}+64=9^{2}$$

Calculate 9 to the power of 2 and get 81.

$$x^{2}+64=81$$

Subtract 81 from both sides.

$$x^{2}+64-81=0$$

Subtract 81 from 64 to get -17.

$$x^{2}-17=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -17 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-17\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-17\right)}}{2}$$

Multiply -4 times -17.

$$x=\frac{0±\sqrt{68}}{2}$$

Take the square root of 68.

$$x=\frac{0±2\sqrt{17}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{17}}{2} when ± is plus.

$$x=\sqrt{17}$$

Now solve the equation x=\frac{0±2\sqrt{17}}{2} when ± is minus.

$$x=-\sqrt{17}$$

The equation is now solved.

$$x=\sqrt{17} x=-\sqrt{17}$$