Solve 5d^2=2d

$$5 d ^ { 2 } = 2 d$$

Solve for d

$$d=\frac{2}{5}=0.4$$

$$d=0$$

Steps Using Factoring

Subtract 2d from both sides.

$$5d^{2}-2d=0$$

Factor out d.

$$d\left(5d-2\right)=0$$

To find equation solutions, solve d=0 and 5d-2=0.

$$d=0 d=\frac{2}{5}$$

Steps Using the Quadratic Formula

Subtract 2d from both sides.

$$5d^{2}-2d=0$$

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

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

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

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

The opposite of -2 is 2.

$$d=\frac{2±2}{2\times 5}$$

Multiply 2 times 5.

$$d=\frac{2±2}{10}$$

Now solve the equation d=\frac{2±2}{10} when ± is plus. Add 2 to 2.

$$d=\frac{4}{10}$$

Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

$$d=\frac{2}{5}$$

Now solve the equation d=\frac{2±2}{10} when ± is minus. Subtract 2 from 2.

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

Divide 0 by 10.

$$d=0$$

The equation is now solved.

$$d=\frac{2}{5} d=0$$

Steps for Completing the Square

Subtract 2d from both sides.

$$5d^{2}-2d=0$$

Divide both sides by 5.

$$\frac{5d^{2}-2d}{5}=\frac{0}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$d^{2}-\frac{2}{5}d=\frac{0}{5}$$

Divide 0 by 5.

$$d^{2}-\frac{2}{5}d=0$$

Divide -\frac{2}{5}, the coefficient of the x term, by 2 to get -\frac{1}{5}. Then add the square of -\frac{1}{5} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$d^{2}-\frac{2}{5}d+\left(-\frac{1}{5}\right)^{2}=\left(-\frac{1}{5}\right)^{2}$$

Square -\frac{1}{5} by squaring both the numerator and the denominator of the fraction.

$$d^{2}-\frac{2}{5}d+\frac{1}{25}=\frac{1}{25}$$

Factor d^{2}-\frac{2}{5}d+\frac{1}{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}.

$$\left(d-\frac{1}{5}\right)^{2}=\frac{1}{25}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(d-\frac{1}{5}\right)^{2}}=\sqrt{\frac{1}{25}}$$

Simplify.

$$d-\frac{1}{5}=\frac{1}{5} d-\frac{1}{5}=-\frac{1}{5}$$

Add \frac{1}{5} to both sides of the equation.

$$d=\frac{2}{5} d=0$$