Solve 9^2=x^2+4^2

$$9 ^ { 2 } = x ^ { 2 } + 4 ^ { 2 }$$

Solve for x

$$x=\sqrt{65}\approx 8.062257748$$

$$x=-\sqrt{65}\approx -8.062257748$$

Steps by Finding Square Root

Calculate 9 to the power of 2 and get 81.

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

Calculate 4 to the power of 2 and get 16.

$$81=x^{2}+16$$

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

$$x^{2}+16=81$$

Subtract 16 from both sides.

$$x^{2}=81-16$$

Subtract 16 from 81 to get 65.

$$x^{2}=65$$

Take the square root of both sides of the equation.

$$x=\sqrt{65} x=-\sqrt{65}$$

Steps Using the Quadratic Formula

Calculate 9 to the power of 2 and get 81.

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

Calculate 4 to the power of 2 and get 16.

$$81=x^{2}+16$$

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

$$x^{2}+16=81$$

Subtract 81 from both sides.

$$x^{2}+16-81=0$$

Subtract 81 from 16 to get -65.

$$x^{2}-65=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -65 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-65\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-65\right)}}{2}$$

Multiply -4 times -65.

$$x=\frac{0±\sqrt{260}}{2}$$

Take the square root of 260.

$$x=\frac{0±2\sqrt{65}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{65}}{2} when ± is plus.

$$x=\sqrt{65}$$

Now solve the equation x=\frac{0±2\sqrt{65}}{2} when ± is minus.

$$x=-\sqrt{65}$$

The equation is now solved.

$$x=\sqrt{65} x=-\sqrt{65}$$