Solve 20^2+55^2=c^2

$$20 ^ { 2 } + 55 ^ { 2 } = c ^ { 2 }$$

Solve for c

$$c=5\sqrt{137}\approx 58.523499554$$

$$c=-5\sqrt{137}\approx -58.523499554$$

Steps by Finding Square Root

Calculate 20 to the power of 2 and get 400.

$$400+55^{2}=c^{2}$$

Calculate 55 to the power of 2 and get 3025.

$$400+3025=c^{2}$$

Add 400 and 3025 to get 3425.

$$3425=c^{2}$$

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

$$c^{2}=3425$$

Take the square root of both sides of the equation.

$$c=5\sqrt{137} c=-5\sqrt{137}$$

Steps Using the Quadratic Formula

Calculate 20 to the power of 2 and get 400.

$$400+55^{2}=c^{2}$$

Calculate 55 to the power of 2 and get 3025.

$$400+3025=c^{2}$$

Add 400 and 3025 to get 3425.

$$3425=c^{2}$$

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

$$c^{2}=3425$$

Subtract 3425 from both sides.

$$c^{2}-3425=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -3425 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-3425\right)}}{2}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-3425\right)}}{2}$$

Multiply -4 times -3425.

$$c=\frac{0±\sqrt{13700}}{2}$$

Take the square root of 13700.

$$c=\frac{0±10\sqrt{137}}{2}$$

Now solve the equation c=\frac{0±10\sqrt{137}}{2} when ± is plus.

$$c=5\sqrt{137}$$

Now solve the equation c=\frac{0±10\sqrt{137}}{2} when ± is minus.

$$c=-5\sqrt{137}$$

The equation is now solved.

$$c=5\sqrt{137} c=-5\sqrt{137}$$