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

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

Solve for x

$$x=\sqrt{85}\approx 9.219544457$$

$$x=-\sqrt{85}\approx -9.219544457$$

Steps by Finding Square Root

Calculate 9 to the power of 2 and get 81.

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

Calculate 2 to the power of 2 and get 4.

$$81+4=x^{2}$$

Add 81 and 4 to get 85.

$$85=x^{2}$$

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

$$x^{2}=85$$

Take the square root of both sides of the equation.

$$x=\sqrt{85} x=-\sqrt{85}$$

Steps Using the Quadratic Formula

Calculate 9 to the power of 2 and get 81.

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

Calculate 2 to the power of 2 and get 4.

$$81+4=x^{2}$$

Add 81 and 4 to get 85.

$$85=x^{2}$$

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

$$x^{2}=85$$

Subtract 85 from both sides.

$$x^{2}-85=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -85 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-85\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-85\right)}}{2}$$

Multiply -4 times -85.

$$x=\frac{0±\sqrt{340}}{2}$$

Take the square root of 340.

$$x=\frac{0±2\sqrt{85}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{85}}{2} when ± is plus.

$$x=\sqrt{85}$$

Now solve the equation x=\frac{0±2\sqrt{85}}{2} when ± is minus.

$$x=-\sqrt{85}$$

The equation is now solved.

$$x=\sqrt{85} x=-\sqrt{85}$$