Solve 10^2+10^2=c^2

$$10 ^ { 2 } + 10 ^ { 2 } = c ^ { 2 }$$

Solve for c

$$c=10\sqrt{2}\approx 14.142135624$$

$$c=-10\sqrt{2}\approx -14.142135624$$

Steps by Finding Square Root

Calculate 10 to the power of 2 and get 100.

$$100+10^{2}=c^{2}$$

Calculate 10 to the power of 2 and get 100.

$$100+100=c^{2}$$

Add 100 and 100 to get 200.

$$200=c^{2}$$

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

$$c^{2}=200$$

Take the square root of both sides of the equation.

$$c=10\sqrt{2} c=-10\sqrt{2}$$

Steps Using the Quadratic Formula

Calculate 10 to the power of 2 and get 100.

$$100+10^{2}=c^{2}$$

Calculate 10 to the power of 2 and get 100.

$$100+100=c^{2}$$

Add 100 and 100 to get 200.

$$200=c^{2}$$

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

$$c^{2}=200$$

Subtract 200 from both sides.

$$c^{2}-200=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -200 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-200\right)}}{2}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-200\right)}}{2}$$

Multiply -4 times -200.

$$c=\frac{0±\sqrt{800}}{2}$$

Take the square root of 800.

$$c=\frac{0±20\sqrt{2}}{2}$$

Now solve the equation c=\frac{0±20\sqrt{2}}{2} when ± is plus.

$$c=10\sqrt{2}$$

Now solve the equation c=\frac{0±20\sqrt{2}}{2} when ± is minus.

$$c=-10\sqrt{2}$$

The equation is now solved.

$$c=10\sqrt{2} c=-10\sqrt{2}$$