Solve 7^2+10^2=c^2

$$7 ^ { 2 } + 10 ^ { 2 } = c ^ { 2 }$$

Solve for c

$$c=\sqrt{149}\approx 12.206555616$$

$$c=-\sqrt{149}\approx -12.206555616$$

Steps by Finding Square Root

Calculate 7 to the power of 2 and get 49.

$$49+10^{2}=c^{2}$$

Calculate 10 to the power of 2 and get 100.

$$49+100=c^{2}$$

Add 49 and 100 to get 149.

$$149=c^{2}$$

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

$$c^{2}=149$$

Take the square root of both sides of the equation.

$$c=\sqrt{149} c=-\sqrt{149}$$

Steps Using the Quadratic Formula

Calculate 7 to the power of 2 and get 49.

$$49+10^{2}=c^{2}$$

Calculate 10 to the power of 2 and get 100.

$$49+100=c^{2}$$

Add 49 and 100 to get 149.

$$149=c^{2}$$

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

$$c^{2}=149$$

Subtract 149 from both sides.

$$c^{2}-149=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -149 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-149\right)}}{2}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-149\right)}}{2}$$

Multiply -4 times -149.

$$c=\frac{0±\sqrt{596}}{2}$$

Take the square root of 596.

$$c=\frac{0±2\sqrt{149}}{2}$$

Now solve the equation c=\frac{0±2\sqrt{149}}{2} when ± is plus.

$$c=\sqrt{149}$$

Now solve the equation c=\frac{0±2\sqrt{149}}{2} when ± is minus.

$$c=-\sqrt{149}$$

The equation is now solved.

$$c=\sqrt{149} c=-\sqrt{149}$$