Solve 6^2+20^2=c^2

$$6 ^ { 2 } + 20 ^ { 2 } = c ^ { 2 }$$

Solve for c

$$c=2\sqrt{109}\approx 20.880613018$$

$$c=-2\sqrt{109}\approx -20.880613018$$

Steps by Finding Square Root

Calculate 6 to the power of 2 and get 36.

$$36+20^{2}=c^{2}$$

Calculate 20 to the power of 2 and get 400.

$$36+400=c^{2}$$

Add 36 and 400 to get 436.

$$436=c^{2}$$

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

$$c^{2}=436$$

Take the square root of both sides of the equation.

$$c=2\sqrt{109} c=-2\sqrt{109}$$

Steps Using the Quadratic Formula

Calculate 6 to the power of 2 and get 36.

$$36+20^{2}=c^{2}$$

Calculate 20 to the power of 2 and get 400.

$$36+400=c^{2}$$

Add 36 and 400 to get 436.

$$436=c^{2}$$

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

$$c^{2}=436$$

Subtract 436 from both sides.

$$c^{2}-436=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -436 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-436\right)}}{2}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-436\right)}}{2}$$

Multiply -4 times -436.

$$c=\frac{0±\sqrt{1744}}{2}$$

Take the square root of 1744.

$$c=\frac{0±4\sqrt{109}}{2}$$

Now solve the equation c=\frac{0±4\sqrt{109}}{2} when ± is plus.

$$c=2\sqrt{109}$$

Now solve the equation c=\frac{0±4\sqrt{109}}{2} when ± is minus.

$$c=-2\sqrt{109}$$

The equation is now solved.

$$c=2\sqrt{109} c=-2\sqrt{109}$$