Solve 20^2+22^2=c^2

$$20 ^ { 2 } + 22 ^ { 2 } = c ^ { 2 }$$

Solve for c

$$c=2\sqrt{221}\approx 29.732137495$$

$$c=-2\sqrt{221}\approx -29.732137495$$

Steps by Finding Square Root

Calculate 20 to the power of 2 and get 400.

$$400+22^{2}=c^{2}$$

Calculate 22 to the power of 2 and get 484.

$$400+484=c^{2}$$

Add 400 and 484 to get 884.

$$884=c^{2}$$

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

$$c^{2}=884$$

Take the square root of both sides of the equation.

$$c=2\sqrt{221} c=-2\sqrt{221}$$

Steps Using the Quadratic Formula

Calculate 20 to the power of 2 and get 400.

$$400+22^{2}=c^{2}$$

Calculate 22 to the power of 2 and get 484.

$$400+484=c^{2}$$

Add 400 and 484 to get 884.

$$884=c^{2}$$

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

$$c^{2}=884$$

Subtract 884 from both sides.

$$c^{2}-884=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -884 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-884\right)}}{2}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-884\right)}}{2}$$

Multiply -4 times -884.

$$c=\frac{0±\sqrt{3536}}{2}$$

Take the square root of 3536.

$$c=\frac{0±4\sqrt{221}}{2}$$

Now solve the equation c=\frac{0±4\sqrt{221}}{2} when ± is plus.

$$c=2\sqrt{221}$$

Now solve the equation c=\frac{0±4\sqrt{221}}{2} when ± is minus.

$$c=-2\sqrt{221}$$

The equation is now solved.

$$c=2\sqrt{221} c=-2\sqrt{221}$$