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

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

Solve for c

$$c=20\sqrt{2}\approx 28.284271247$$

$$c=-20\sqrt{2}\approx -28.284271247$$

Steps by Finding Square Root

Calculate 20 to the power of 2 and get 400.

$$400+20^{2}=c^{2}$$

Calculate 20 to the power of 2 and get 400.

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

Add 400 and 400 to get 800.

$$800=c^{2}$$

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

$$c^{2}=800$$

Take the square root of both sides of the equation.

$$c=20\sqrt{2} c=-20\sqrt{2}$$

Steps Using the Quadratic Formula

Calculate 20 to the power of 2 and get 400.

$$400+20^{2}=c^{2}$$

Calculate 20 to the power of 2 and get 400.

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

Add 400 and 400 to get 800.

$$800=c^{2}$$

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

$$c^{2}=800$$

Subtract 800 from both sides.

$$c^{2}-800=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -800 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-800\right)}}{2}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-800\right)}}{2}$$

Multiply -4 times -800.

$$c=\frac{0±\sqrt{3200}}{2}$$

Take the square root of 3200.

$$c=\frac{0±40\sqrt{2}}{2}$$

Now solve the equation c=\frac{0±40\sqrt{2}}{2} when ± is plus.

$$c=20\sqrt{2}$$

Now solve the equation c=\frac{0±40\sqrt{2}}{2} when ± is minus.

$$c=-20\sqrt{2}$$

The equation is now solved.

$$c=20\sqrt{2} c=-20\sqrt{2}$$