Solve c^2-c^2/4=400

$$c ^ { 2 } - \frac { c ^ { 2 } } { 4 } = 400$$

Solve for c

$$c = \frac{40 \sqrt{3}}{3} \approx 23.094010768$$

$$c = -\frac{40 \sqrt{3}}{3} \approx -23.094010768$$

Steps by Finding Square Root

Multiply both sides of the equation by 4.

$$4c^{2}-c^{2}=1600$$

Combine 4c^{2} and -c^{2} to get 3c^{2}.

$$3c^{2}=1600$$

Divide both sides by 3.

$$c^{2}=\frac{1600}{3}$$

Take the square root of both sides of the equation.

$$c=\frac{40\sqrt{3}}{3} c=-\frac{40\sqrt{3}}{3}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 4.

$$4c^{2}-c^{2}=1600$$

Subtract 1600 from both sides.

$$4c^{2}-c^{2}-1600=0$$

Combine 4c^{2} and -c^{2} to get 3c^{2}.

$$3c^{2}-1600=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -1600 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\times 3\left(-1600\right)}}{2\times 3}$$

Square 0.

$$c=\frac{0±\sqrt{-4\times 3\left(-1600\right)}}{2\times 3}$$

Multiply -4 times 3.

$$c=\frac{0±\sqrt{-12\left(-1600\right)}}{2\times 3}$$

Multiply -12 times -1600.

$$c=\frac{0±\sqrt{19200}}{2\times 3}$$

Take the square root of 19200.

$$c=\frac{0±80\sqrt{3}}{2\times 3}$$

Multiply 2 times 3.

$$c=\frac{0±80\sqrt{3}}{6}$$

Now solve the equation c=\frac{0±80\sqrt{3}}{6} when ± is plus.

$$c=\frac{40\sqrt{3}}{3}$$

Now solve the equation c=\frac{0±80\sqrt{3}}{6} when ± is minus.

$$c=-\frac{40\sqrt{3}}{3}$$

The equation is now solved.

$$c=\frac{40\sqrt{3}}{3} c=-\frac{40\sqrt{3}}{3}$$