Solve 8^2+15^2=c^2

$$8 ^ { 2 } + 15 ^ { 2 } = c ^ { 2 }$$

Solve for c

$$c=17$$

$$c=-17$$

Steps Using Difference of Squares

Calculate 8 to the power of 2 and get 64.

$$64+15^{2}=c^{2}$$

Calculate 15 to the power of 2 and get 225.

$$64+225=c^{2}$$

Add 64 and 225 to get 289.

$$289=c^{2}$$

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

$$c^{2}=289$$

Subtract 289 from both sides.

$$c^{2}-289=0$$

Consider c^{2}-289. Rewrite c^{2}-289 as c^{2}-17^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(c-17\right)\left(c+17\right)=0$$

To find equation solutions, solve c-17=0 and c+17=0.

$$c=17 c=-17$$

Steps by Finding Square Root

Calculate 8 to the power of 2 and get 64.

$$64+15^{2}=c^{2}$$

Calculate 15 to the power of 2 and get 225.

$$64+225=c^{2}$$

Add 64 and 225 to get 289.

$$289=c^{2}$$

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

$$c^{2}=289$$

Take the square root of both sides of the equation.

$$c=17 c=-17$$

Steps Using the Quadratic Formula

Calculate 8 to the power of 2 and get 64.

$$64+15^{2}=c^{2}$$

Calculate 15 to the power of 2 and get 225.

$$64+225=c^{2}$$

Add 64 and 225 to get 289.

$$289=c^{2}$$

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

$$c^{2}=289$$

Subtract 289 from both sides.

$$c^{2}-289=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -289 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-289\right)}}{2}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-289\right)}}{2}$$

Multiply -4 times -289.

$$c=\frac{0±\sqrt{1156}}{2}$$

Take the square root of 1156.

$$c=\frac{0±34}{2}$$

Now solve the equation c=\frac{0±34}{2} when ± is plus. Divide 34 by 2.

$$c=17$$

Now solve the equation c=\frac{0±34}{2} when ± is minus. Divide -34 by 2.

$$c=-17$$

The equation is now solved.

$$c=17 c=-17$$