Solve c^2=13^2+84^2

$$c ^ { 2 } = 13 ^ { 2 } + 84 ^ { 2 }$$

Solve for c

$$c=-85$$

$$c=85$$

Steps Using Difference of Squares

Calculate 13 to the power of 2 and get 169.

$$c^{2}=169+84^{2}$$

Calculate 84 to the power of 2 and get 7056.

$$c^{2}=169+7056$$

Add 169 and 7056 to get 7225.

$$c^{2}=7225$$

Subtract 7225 from both sides.

$$c^{2}-7225=0$$

Consider c^{2}-7225. Rewrite c^{2}-7225 as c^{2}-85^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(c-85\right)\left(c+85\right)=0$$

To find equation solutions, solve c-85=0 and c+85=0.

$$c=85 c=-85$$

Steps by Finding Square Root

Calculate 13 to the power of 2 and get 169.

$$c^{2}=169+84^{2}$$

Calculate 84 to the power of 2 and get 7056.

$$c^{2}=169+7056$$

Add 169 and 7056 to get 7225.

$$c^{2}=7225$$

Take the square root of both sides of the equation.

$$c=85 c=-85$$

Steps Using the Quadratic Formula

Calculate 13 to the power of 2 and get 169.

$$c^{2}=169+84^{2}$$

Calculate 84 to the power of 2 and get 7056.

$$c^{2}=169+7056$$

Add 169 and 7056 to get 7225.

$$c^{2}=7225$$

Subtract 7225 from both sides.

$$c^{2}-7225=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -7225 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-7225\right)}}{2}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-7225\right)}}{2}$$

Multiply -4 times -7225.

$$c=\frac{0±\sqrt{28900}}{2}$$

Take the square root of 28900.

$$c=\frac{0±170}{2}$$

Now solve the equation c=\frac{0±170}{2} when ± is plus. Divide 170 by 2.

$$c=85$$

Now solve the equation c=\frac{0±170}{2} when ± is minus. Divide -170 by 2.

$$c=-85$$

The equation is now solved.

$$c=85 c=-85$$