Solve 13^2+9^2=c^2

$$13 ^ { 2 } + 9 ^ { 2 } = c ^ { 2 }$$

Solve for c

$$c=5\sqrt{10}\approx 15.811388301$$

$$c=-5\sqrt{10}\approx -15.811388301$$

Steps by Finding Square Root

Calculate 13 to the power of 2 and get 169.

$$169+9^{2}=c^{2}$$

Calculate 9 to the power of 2 and get 81.

$$169+81=c^{2}$$

Add 169 and 81 to get 250.

$$250=c^{2}$$

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

$$c^{2}=250$$

Take the square root of both sides of the equation.

$$c=5\sqrt{10} c=-5\sqrt{10}$$

Steps Using the Quadratic Formula

Calculate 13 to the power of 2 and get 169.

$$169+9^{2}=c^{2}$$

Calculate 9 to the power of 2 and get 81.

$$169+81=c^{2}$$

Add 169 and 81 to get 250.

$$250=c^{2}$$

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

$$c^{2}=250$$

Subtract 250 from both sides.

$$c^{2}-250=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -250 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-250\right)}}{2}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-250\right)}}{2}$$

Multiply -4 times -250.

$$c=\frac{0±\sqrt{1000}}{2}$$

Take the square root of 1000.

$$c=\frac{0±10\sqrt{10}}{2}$$

Now solve the equation c=\frac{0±10\sqrt{10}}{2} when ± is plus.

$$c=5\sqrt{10}$$

Now solve the equation c=\frac{0±10\sqrt{10}}{2} when ± is minus.

$$c=-5\sqrt{10}$$

The equation is now solved.

$$c=5\sqrt{10} c=-5\sqrt{10}$$