Solve 12^2+13^2=c^2

$$12 ^ { 2 } + 13 ^ { 2 } = c ^ { 2 }$$

Solve for c

$$c=\sqrt{313}\approx 17.691806013$$

$$c=-\sqrt{313}\approx -17.691806013$$

Steps by Finding Square Root

Calculate 12 to the power of 2 and get 144.

$$144+13^{2}=c^{2}$$

Calculate 13 to the power of 2 and get 169.

$$144+169=c^{2}$$

Add 144 and 169 to get 313.

$$313=c^{2}$$

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

$$c^{2}=313$$

Take the square root of both sides of the equation.

$$c=\sqrt{313} c=-\sqrt{313}$$

Steps Using the Quadratic Formula

Calculate 12 to the power of 2 and get 144.

$$144+13^{2}=c^{2}$$

Calculate 13 to the power of 2 and get 169.

$$144+169=c^{2}$$

Add 144 and 169 to get 313.

$$313=c^{2}$$

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

$$c^{2}=313$$

Subtract 313 from both sides.

$$c^{2}-313=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -313 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-313\right)}}{2}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-313\right)}}{2}$$

Multiply -4 times -313.

$$c=\frac{0±\sqrt{1252}}{2}$$

Take the square root of 1252.

$$c=\frac{0±2\sqrt{313}}{2}$$

Now solve the equation c=\frac{0±2\sqrt{313}}{2} when ± is plus.

$$c=\sqrt{313}$$

Now solve the equation c=\frac{0±2\sqrt{313}}{2} when ± is minus.

$$c=-\sqrt{313}$$

The equation is now solved.

$$c=\sqrt{313} c=-\sqrt{313}$$