Solve x^2=7^2+16

$$x ^ { 2 } = 7 ^ { 2 } + 16$$

Solve for x

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

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

Steps by Finding Square Root

Calculate 7 to the power of 2 and get 49.

$$x^{2}=49+16$$

Add 49 and 16 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 7 to the power of 2 and get 49.

$$x^{2}=49+16$$

Add 49 and 16 to get 65.

$$x^{2}=65$$

Subtract 65 from both sides.

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

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.

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