Solve 13^2+29=c^2

$$13 ^ { 2 } + 29 = c ^ { 2 }$$

Solve for c

$$c=3\sqrt{22}\approx 14.071247279$$

$$c=-3\sqrt{22}\approx -14.071247279$$

Steps by Finding Square Root

Calculate 13 to the power of 2 and get 169.

$$169+29=c^{2}$$

Add 169 and 29 to get 198.

$$198=c^{2}$$

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

$$c^{2}=198$$

Take the square root of both sides of the equation.

$$c=3\sqrt{22} c=-3\sqrt{22}$$

Steps Using the Quadratic Formula

Calculate 13 to the power of 2 and get 169.

$$169+29=c^{2}$$

Add 169 and 29 to get 198.

$$198=c^{2}$$

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

$$c^{2}=198$$

Subtract 198 from both sides.

$$c^{2}-198=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -198 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-198\right)}}{2}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-198\right)}}{2}$$

Multiply -4 times -198.

$$c=\frac{0±\sqrt{792}}{2}$$

Take the square root of 792.

$$c=\frac{0±6\sqrt{22}}{2}$$

Now solve the equation c=\frac{0±6\sqrt{22}}{2} when ± is plus.

$$c=3\sqrt{22}$$

Now solve the equation c=\frac{0±6\sqrt{22}}{2} when ± is minus.

$$c=-3\sqrt{22}$$

The equation is now solved.

$$c=3\sqrt{22} c=-3\sqrt{22}$$