Solve 7c^2=100

$$7 c ^ { 2 } = 100$$

Solve for c

$$c = \frac{10 \sqrt{7}}{7} \approx 3.77964473$$

$$c = -\frac{10 \sqrt{7}}{7} \approx -3.77964473$$

Steps by Finding Square Root

Divide both sides by 7.

$$c^{2}=\frac{100}{7}$$

Take the square root of both sides of the equation.

$$c=\frac{10\sqrt{7}}{7} c=-\frac{10\sqrt{7}}{7}$$

Steps Using the Quadratic Formula

Divide both sides by 7.

$$c^{2}=\frac{100}{7}$$

Subtract \frac{100}{7} from both sides.

$$c^{2}-\frac{100}{7}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{100}{7} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-\frac{100}{7}\right)}}{2}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-\frac{100}{7}\right)}}{2}$$

Multiply -4 times -\frac{100}{7}.

$$c=\frac{0±\sqrt{\frac{400}{7}}}{2}$$

Take the square root of \frac{400}{7}.

$$c=\frac{0±\frac{20\sqrt{7}}{7}}{2}$$

Now solve the equation c=\frac{0±\frac{20\sqrt{7}}{7}}{2} when ± is plus.

$$c=\frac{10\sqrt{7}}{7}$$

Now solve the equation c=\frac{0±\frac{20\sqrt{7}}{7}}{2} when ± is minus.

$$c=-\frac{10\sqrt{7}}{7}$$

The equation is now solved.

$$c=\frac{10\sqrt{7}}{7} c=-\frac{10\sqrt{7}}{7}$$