Solve 4y^2=28y

$$4 y ^ { 2 } = 28 y$$

Solve for y

$$y=7$$

$$y=0$$

Steps Using Factoring

Subtract 28y from both sides.

$$4y^{2}-28y=0$$

Factor out y.

$$y\left(4y-28\right)=0$$

To find equation solutions, solve y=0 and 4y-28=0.

$$y=0 y=7$$

Steps Using the Quadratic Formula

Subtract 28y from both sides.

$$4y^{2}-28y=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, -28 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{-\left(-28\right)±\sqrt{\left(-28\right)^{2}}}{2\times 4}$$

Take the square root of \left(-28\right)^{2}.

$$y=\frac{-\left(-28\right)±28}{2\times 4}$$

The opposite of -28 is 28.

$$y=\frac{28±28}{2\times 4}$$

Multiply 2 times 4.

$$y=\frac{28±28}{8}$$

Now solve the equation y=\frac{28±28}{8} when ± is plus. Add 28 to 28.

$$y=\frac{56}{8}$$

Divide 56 by 8.

$$y=7$$

Now solve the equation y=\frac{28±28}{8} when ± is minus. Subtract 28 from 28.

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

Divide 0 by 8.

$$y=0$$

The equation is now solved.

$$y=7 y=0$$

Steps for Completing the Square

Subtract 28y from both sides.

$$4y^{2}-28y=0$$

Divide both sides by 4.

$$\frac{4y^{2}-28y}{4}=\frac{0}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$y^{2}+\left(-\frac{28}{4}\right)y=\frac{0}{4}$$

Divide -28 by 4.

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

Divide 0 by 4.

$$y^{2}-7y=0$$

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

$$y^{2}-7y+\left(-\frac{7}{2}\right)^{2}=\left(-\frac{7}{2}\right)^{2}$$

Square -\frac{7}{2} by squaring both the numerator and the denominator of the fraction.

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

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

$$\left(y-\frac{7}{2}\right)^{2}=\frac{49}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(y-\frac{7}{2}\right)^{2}}=\sqrt{\frac{49}{4}}$$

Simplify.

$$y-\frac{7}{2}=\frac{7}{2} y-\frac{7}{2}=-\frac{7}{2}$$

Add \frac{7}{2} to both sides of the equation.

$$y=7 y=0$$