Solve 13^2+29^2=c^2

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

Solve for c

$$c=\sqrt{1010}\approx 31.780497164$$

$$c=-\sqrt{1010}\approx -31.780497164$$

Steps by Finding Square Root

Calculate 13 to the power of 2 and get 169.

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

Calculate 29 to the power of 2 and get 841.

$$169+841=c^{2}$$

Add 169 and 841 to get 1010.

$$1010=c^{2}$$

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

$$c^{2}=1010$$

Take the square root of both sides of the equation.

$$c=\sqrt{1010} c=-\sqrt{1010}$$

Steps Using the Quadratic Formula

Calculate 13 to the power of 2 and get 169.

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

Calculate 29 to the power of 2 and get 841.

$$169+841=c^{2}$$

Add 169 and 841 to get 1010.

$$1010=c^{2}$$

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

$$c^{2}=1010$$

Subtract 1010 from both sides.

$$c^{2}-1010=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -1010 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-1010\right)}}{2}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-1010\right)}}{2}$$

Multiply -4 times -1010.

$$c=\frac{0±\sqrt{4040}}{2}$$

Take the square root of 4040.

$$c=\frac{0±2\sqrt{1010}}{2}$$

Now solve the equation c=\frac{0±2\sqrt{1010}}{2} when ± is plus.

$$c=\sqrt{1010}$$

Now solve the equation c=\frac{0±2\sqrt{1010}}{2} when ± is minus.

$$c=-\sqrt{1010}$$

The equation is now solved.

$$c=\sqrt{1010} c=-\sqrt{1010}$$