Solve c^2=13^2+15

$$c ^ { 2 } = 13 ^ { 2 } + 15$$

Solve for c

$$c=2\sqrt{46}\approx 13.564659966$$

$$c=-2\sqrt{46}\approx -13.564659966$$

Steps by Finding Square Root

Calculate 13 to the power of 2 and get 169.

$$c^{2}=169+15$$

Add 169 and 15 to get 184.

$$c^{2}=184$$

Take the square root of both sides of the equation.

$$c=2\sqrt{46} c=-2\sqrt{46}$$

Steps Using the Quadratic Formula

Calculate 13 to the power of 2 and get 169.

$$c^{2}=169+15$$

Add 169 and 15 to get 184.

$$c^{2}=184$$

Subtract 184 from both sides.

$$c^{2}-184=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -184 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-184\right)}}{2}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-184\right)}}{2}$$

Multiply -4 times -184.

$$c=\frac{0±\sqrt{736}}{2}$$

Take the square root of 736.

$$c=\frac{0±4\sqrt{46}}{2}$$

Now solve the equation c=\frac{0±4\sqrt{46}}{2} when ± is plus.

$$c=2\sqrt{46}$$

Now solve the equation c=\frac{0±4\sqrt{46}}{2} when ± is minus.

$$c=-2\sqrt{46}$$

The equation is now solved.

$$c=2\sqrt{46} c=-2\sqrt{46}$$