Solve 5c^2=8c

$$5 c ^ { 2 } = 8 c$$

Solve for c

$$c = \frac{8}{5} = 1\frac{3}{5} = 1.6$$

$$c=0$$

Steps Using Factoring

Subtract 8c from both sides.

$$5c^{2}-8c=0$$

Factor out c.

$$c\left(5c-8\right)=0$$

To find equation solutions, solve c=0 and 5c-8=0.

$$c=0 c=\frac{8}{5}$$

Steps Using the Quadratic Formula

Subtract 8c from both sides.

$$5c^{2}-8c=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, -8 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}}}{2\times 5}$$

Take the square root of \left(-8\right)^{2}.

$$c=\frac{-\left(-8\right)±8}{2\times 5}$$

The opposite of -8 is 8.

$$c=\frac{8±8}{2\times 5}$$

Multiply 2 times 5.

$$c=\frac{8±8}{10}$$

Now solve the equation c=\frac{8±8}{10} when ± is plus. Add 8 to 8.

$$c=\frac{16}{10}$$

Reduce the fraction \frac{16}{10} to lowest terms by extracting and canceling out 2.

$$c=\frac{8}{5}$$

Now solve the equation c=\frac{8±8}{10} when ± is minus. Subtract 8 from 8.

$$c=\frac{0}{10}$$

Divide 0 by 10.

$$c=0$$

The equation is now solved.

$$c=\frac{8}{5} c=0$$

Steps for Completing the Square

Subtract 8c from both sides.

$$5c^{2}-8c=0$$

Divide both sides by 5.

$$\frac{5c^{2}-8c}{5}=\frac{0}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$c^{2}-\frac{8}{5}c=\frac{0}{5}$$

Divide 0 by 5.

$$c^{2}-\frac{8}{5}c=0$$

Divide -\frac{8}{5}, the coefficient of the x term, by 2 to get -\frac{4}{5}. Then add the square of -\frac{4}{5} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$c^{2}-\frac{8}{5}c+\left(-\frac{4}{5}\right)^{2}=\left(-\frac{4}{5}\right)^{2}$$

Square -\frac{4}{5} by squaring both the numerator and the denominator of the fraction.

$$c^{2}-\frac{8}{5}c+\frac{16}{25}=\frac{16}{25}$$

Factor c^{2}-\frac{8}{5}c+\frac{16}{25}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(c-\frac{4}{5}\right)^{2}=\frac{16}{25}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(c-\frac{4}{5}\right)^{2}}=\sqrt{\frac{16}{25}}$$

Simplify.

$$c-\frac{4}{5}=\frac{4}{5} c-\frac{4}{5}=-\frac{4}{5}$$

Add \frac{4}{5} to both sides of the equation.

$$c=\frac{8}{5} c=0$$