Solve 5^2+12^2=c^2

$$5 ^ { 2 } + 12 ^ { 2 } = c ^ { 2 }$$

Solve for c

$$c=13$$

$$c=-13$$

Steps Using Difference of Squares

Calculate 5 to the power of 2 and get 25.

$$25+12^{2}=c^{2}$$

Calculate 12 to the power of 2 and get 144.

$$25+144=c^{2}$$

Add 25 and 144 to get 169.

$$169=c^{2}$$

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

$$c^{2}=169$$

Subtract 169 from both sides.

$$c^{2}-169=0$$

Consider c^{2}-169. Rewrite c^{2}-169 as c^{2}-13^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(c-13\right)\left(c+13\right)=0$$

To find equation solutions, solve c-13=0 and c+13=0.

$$c=13 c=-13$$

Steps by Finding Square Root

Calculate 5 to the power of 2 and get 25.

$$25+12^{2}=c^{2}$$

Calculate 12 to the power of 2 and get 144.

$$25+144=c^{2}$$

Add 25 and 144 to get 169.

$$169=c^{2}$$

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

$$c^{2}=169$$

Take the square root of both sides of the equation.

$$c=13 c=-13$$

Steps Using the Quadratic Formula

Calculate 5 to the power of 2 and get 25.

$$25+12^{2}=c^{2}$$

Calculate 12 to the power of 2 and get 144.

$$25+144=c^{2}$$

Add 25 and 144 to get 169.

$$169=c^{2}$$

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

$$c^{2}=169$$

Subtract 169 from both sides.

$$c^{2}-169=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -169 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-169\right)}}{2}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-169\right)}}{2}$$

Multiply -4 times -169.

$$c=\frac{0±\sqrt{676}}{2}$$

Take the square root of 676.

$$c=\frac{0±26}{2}$$

Now solve the equation c=\frac{0±26}{2} when ± is plus. Divide 26 by 2.

$$c=13$$

Now solve the equation c=\frac{0±26}{2} when ± is minus. Divide -26 by 2.

$$c=-13$$

The equation is now solved.

$$c=13 c=-13$$