Solve x^2=10^2+9^2

$$x ^ { 2 } = 10 ^ { 2 } + 9 ^ { 2 }$$

Solve for x

$$x=\sqrt{181}\approx 13.453624047$$

$$x=-\sqrt{181}\approx -13.453624047$$

Steps by Finding Square Root

Calculate 10 to the power of 2 and get 100.

$$x^{2}=100+9^{2}$$

Calculate 9 to the power of 2 and get 81.

$$x^{2}=100+81$$

Add 100 and 81 to get 181.

$$x^{2}=181$$

Take the square root of both sides of the equation.

$$x=\sqrt{181} x=-\sqrt{181}$$

Steps Using the Quadratic Formula

Calculate 10 to the power of 2 and get 100.

$$x^{2}=100+9^{2}$$

Calculate 9 to the power of 2 and get 81.

$$x^{2}=100+81$$

Add 100 and 81 to get 181.

$$x^{2}=181$$

Subtract 181 from both sides.

$$x^{2}-181=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -181 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-181\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-181\right)}}{2}$$

Multiply -4 times -181.

$$x=\frac{0±\sqrt{724}}{2}$$

Take the square root of 724.

$$x=\frac{0±2\sqrt{181}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{181}}{2} when ± is plus.

$$x=\sqrt{181}$$

Now solve the equation x=\frac{0±2\sqrt{181}}{2} when ± is minus.

$$x=-\sqrt{181}$$

The equation is now solved.

$$x=\sqrt{181} x=-\sqrt{181}$$