Solve 17^2+28^2=c^2

$$17 ^ { 2 } + 28 ^ { 2 } = c ^ { 2 }$$

Solve for c

$$c=\sqrt{1073}\approx 32.756678708$$

$$c=-\sqrt{1073}\approx -32.756678708$$

Steps by Finding Square Root

Calculate 17 to the power of 2 and get 289.

$$289+28^{2}=c^{2}$$

Calculate 28 to the power of 2 and get 784.

$$289+784=c^{2}$$

Add 289 and 784 to get 1073.

$$1073=c^{2}$$

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

$$c^{2}=1073$$

Take the square root of both sides of the equation.

$$c=\sqrt{1073} c=-\sqrt{1073}$$

Steps Using the Quadratic Formula

Calculate 17 to the power of 2 and get 289.

$$289+28^{2}=c^{2}$$

Calculate 28 to the power of 2 and get 784.

$$289+784=c^{2}$$

Add 289 and 784 to get 1073.

$$1073=c^{2}$$

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

$$c^{2}=1073$$

Subtract 1073 from both sides.

$$c^{2}-1073=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -1073 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-1073\right)}}{2}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-1073\right)}}{2}$$

Multiply -4 times -1073.

$$c=\frac{0±\sqrt{4292}}{2}$$

Take the square root of 4292.

$$c=\frac{0±2\sqrt{1073}}{2}$$

Now solve the equation c=\frac{0±2\sqrt{1073}}{2} when ± is plus.

$$c=\sqrt{1073}$$

Now solve the equation c=\frac{0±2\sqrt{1073}}{2} when ± is minus.

$$c=-\sqrt{1073}$$

The equation is now solved.

$$c=\sqrt{1073} c=-\sqrt{1073}$$