Solve 6^2+7^2=c^2

$$6 ^ { 2 } + 7 ^ { 2 } = c ^ { 2 }$$

Solve for c

$$c=\sqrt{85}\approx 9.219544457$$

$$c=-\sqrt{85}\approx -9.219544457$$

Steps by Finding Square Root

Calculate 6 to the power of 2 and get 36.

$$36+7^{2}=c^{2}$$

Calculate 7 to the power of 2 and get 49.

$$36+49=c^{2}$$

Add 36 and 49 to get 85.

$$85=c^{2}$$

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

$$c^{2}=85$$

Take the square root of both sides of the equation.

$$c=\sqrt{85} c=-\sqrt{85}$$

Steps Using the Quadratic Formula

Calculate 6 to the power of 2 and get 36.

$$36+7^{2}=c^{2}$$

Calculate 7 to the power of 2 and get 49.

$$36+49=c^{2}$$

Add 36 and 49 to get 85.

$$85=c^{2}$$

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

$$c^{2}=85$$

Subtract 85 from both sides.

$$c^{2}-85=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -85 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-85\right)}}{2}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-85\right)}}{2}$$

Multiply -4 times -85.

$$c=\frac{0±\sqrt{340}}{2}$$

Take the square root of 340.

$$c=\frac{0±2\sqrt{85}}{2}$$

Now solve the equation c=\frac{0±2\sqrt{85}}{2} when ± is plus.

$$c=\sqrt{85}$$

Now solve the equation c=\frac{0±2\sqrt{85}}{2} when ± is minus.

$$c=-\sqrt{85}$$

The equation is now solved.

$$c=\sqrt{85} c=-\sqrt{85}$$