Solve 5^2+7^2=c^2

$$5 ^ { 2 } + 7 ^ { 2 } = c ^ { 2 }$$

Solve for c

$$c=\sqrt{74}\approx 8.602325267$$

$$c=-\sqrt{74}\approx -8.602325267$$

Steps by Finding Square Root

Calculate 5 to the power of 2 and get 25.

$$25+7^{2}=c^{2}$$

Calculate 7 to the power of 2 and get 49.

$$25+49=c^{2}$$

Add 25 and 49 to get 74.

$$74=c^{2}$$

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

$$c^{2}=74$$

Take the square root of both sides of the equation.

$$c=\sqrt{74} c=-\sqrt{74}$$

Steps Using the Quadratic Formula

Calculate 5 to the power of 2 and get 25.

$$25+7^{2}=c^{2}$$

Calculate 7 to the power of 2 and get 49.

$$25+49=c^{2}$$

Add 25 and 49 to get 74.

$$74=c^{2}$$

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

$$c^{2}=74$$

Subtract 74 from both sides.

$$c^{2}-74=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -74 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-74\right)}}{2}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-74\right)}}{2}$$

Multiply -4 times -74.

$$c=\frac{0±\sqrt{296}}{2}$$

Take the square root of 296.

$$c=\frac{0±2\sqrt{74}}{2}$$

Now solve the equation c=\frac{0±2\sqrt{74}}{2} when ± is plus.

$$c=\sqrt{74}$$

Now solve the equation c=\frac{0±2\sqrt{74}}{2} when ± is minus.

$$c=-\sqrt{74}$$

The equation is now solved.

$$c=\sqrt{74} c=-\sqrt{74}$$