Solve 4w^2=7w

$$4 w ^ { 2 } = 7 w$$

Solve for w

$$w = \frac{7}{4} = 1\frac{3}{4} = 1.75$$

$$w=0$$

Steps Using Factoring

Subtract 7w from both sides.

$$4w^{2}-7w=0$$

Factor out w.

$$w\left(4w-7\right)=0$$

To find equation solutions, solve w=0 and 4w-7=0.

$$w=0 w=\frac{7}{4}$$

Steps Using the Quadratic Formula

Subtract 7w from both sides.

$$4w^{2}-7w=0$$

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

$$w=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}}}{2\times 4}$$

Take the square root of \left(-7\right)^{2}.

$$w=\frac{-\left(-7\right)±7}{2\times 4}$$

The opposite of -7 is 7.

$$w=\frac{7±7}{2\times 4}$$

Multiply 2 times 4.

$$w=\frac{7±7}{8}$$

Now solve the equation w=\frac{7±7}{8} when ± is plus. Add 7 to 7.

$$w=\frac{14}{8}$$

Reduce the fraction \frac{14}{8} to lowest terms by extracting and canceling out 2.

$$w=\frac{7}{4}$$

Now solve the equation w=\frac{7±7}{8} when ± is minus. Subtract 7 from 7.

$$w=\frac{0}{8}$$

Divide 0 by 8.

$$w=0$$

The equation is now solved.

$$w=\frac{7}{4} w=0$$

Steps for Completing the Square

Subtract 7w from both sides.

$$4w^{2}-7w=0$$

Divide both sides by 4.

$$\frac{4w^{2}-7w}{4}=\frac{0}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$w^{2}-\frac{7}{4}w=\frac{0}{4}$$

Divide 0 by 4.

$$w^{2}-\frac{7}{4}w=0$$

Divide -\frac{7}{4}, the coefficient of the x term, by 2 to get -\frac{7}{8}. Then add the square of -\frac{7}{8} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$w^{2}-\frac{7}{4}w+\left(-\frac{7}{8}\right)^{2}=\left(-\frac{7}{8}\right)^{2}$$

Square -\frac{7}{8} by squaring both the numerator and the denominator of the fraction.

$$w^{2}-\frac{7}{4}w+\frac{49}{64}=\frac{49}{64}$$

Factor w^{2}-\frac{7}{4}w+\frac{49}{64}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(w-\frac{7}{8}\right)^{2}=\frac{49}{64}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(w-\frac{7}{8}\right)^{2}}=\sqrt{\frac{49}{64}}$$

Simplify.

$$w-\frac{7}{8}=\frac{7}{8} w-\frac{7}{8}=-\frac{7}{8}$$

Add \frac{7}{8} to both sides of the equation.

$$w=\frac{7}{4} w=0$$