Solve 9^2+14^2=c^2

$$9 ^ { 2 } + 14 ^ { 2 } = c ^ { 2 }$$

Solve for c

$$c=\sqrt{277}\approx 16.643316977$$

$$c=-\sqrt{277}\approx -16.643316977$$

Steps by Finding Square Root

Calculate 9 to the power of 2 and get 81.

$$81+14^{2}=c^{2}$$

Calculate 14 to the power of 2 and get 196.

$$81+196=c^{2}$$

Add 81 and 196 to get 277.

$$277=c^{2}$$

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

$$c^{2}=277$$

Take the square root of both sides of the equation.

$$c=\sqrt{277} c=-\sqrt{277}$$

Steps Using the Quadratic Formula

Calculate 9 to the power of 2 and get 81.

$$81+14^{2}=c^{2}$$

Calculate 14 to the power of 2 and get 196.

$$81+196=c^{2}$$

Add 81 and 196 to get 277.

$$277=c^{2}$$

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

$$c^{2}=277$$

Subtract 277 from both sides.

$$c^{2}-277=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -277 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-277\right)}}{2}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-277\right)}}{2}$$

Multiply -4 times -277.

$$c=\frac{0±\sqrt{1108}}{2}$$

Take the square root of 1108.

$$c=\frac{0±2\sqrt{277}}{2}$$

Now solve the equation c=\frac{0±2\sqrt{277}}{2} when ± is plus.

$$c=\sqrt{277}$$

Now solve the equation c=\frac{0±2\sqrt{277}}{2} when ± is minus.

$$c=-\sqrt{277}$$

The equation is now solved.

$$c=\sqrt{277} c=-\sqrt{277}$$