Solve 50^2+17^2=c^2

$$50 ^ { 2 } + 17 ^ { 2 } = c ^ { 2 }$$

Solve for c

$$c=\sqrt{2789}\approx 52.810983706$$

$$c=-\sqrt{2789}\approx -52.810983706$$

Steps by Finding Square Root

Calculate 50 to the power of 2 and get 2500.

$$2500+17^{2}=c^{2}$$

Calculate 17 to the power of 2 and get 289.

$$2500+289=c^{2}$$

Add 2500 and 289 to get 2789.

$$2789=c^{2}$$

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

$$c^{2}=2789$$

Take the square root of both sides of the equation.

$$c=\sqrt{2789} c=-\sqrt{2789}$$

Steps Using the Quadratic Formula

Calculate 50 to the power of 2 and get 2500.

$$2500+17^{2}=c^{2}$$

Calculate 17 to the power of 2 and get 289.

$$2500+289=c^{2}$$

Add 2500 and 289 to get 2789.

$$2789=c^{2}$$

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

$$c^{2}=2789$$

Subtract 2789 from both sides.

$$c^{2}-2789=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -2789 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-2789\right)}}{2}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-2789\right)}}{2}$$

Multiply -4 times -2789.

$$c=\frac{0±\sqrt{11156}}{2}$$

Take the square root of 11156.

$$c=\frac{0±2\sqrt{2789}}{2}$$

Now solve the equation c=\frac{0±2\sqrt{2789}}{2} when ± is plus.

$$c=\sqrt{2789}$$

Now solve the equation c=\frac{0±2\sqrt{2789}}{2} when ± is minus.

$$c=-\sqrt{2789}$$

The equation is now solved.

$$c=\sqrt{2789} c=-\sqrt{2789}$$