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

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

Solve for x

$$x=\sqrt{145}\approx 12.041594579$$

$$x=-\sqrt{145}\approx -12.041594579$$

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.

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

Add 64 and 81 to get 145.

$$x^{2}=145$$

Take the square root of both sides of the equation.

$$x=\sqrt{145} x=-\sqrt{145}$$

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.

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

Add 64 and 81 to get 145.

$$x^{2}=145$$

Subtract 145 from both sides.

$$x^{2}-145=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -145 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-145\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-145\right)}}{2}$$

Multiply -4 times -145.

$$x=\frac{0±\sqrt{580}}{2}$$

Take the square root of 580.

$$x=\frac{0±2\sqrt{145}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{145}}{2} when ± is plus.

$$x=\sqrt{145}$$

Now solve the equation x=\frac{0±2\sqrt{145}}{2} when ± is minus.

$$x=-\sqrt{145}$$

The equation is now solved.

$$x=\sqrt{145} x=-\sqrt{145}$$