Solve 4y^2-89y+33y=0

$$4 y ^ { 2 } - 89 y + 33 y = 0$$

Solve for y

$$y=14$$

$$y=0$$

Steps Using Factoring

Factor out y.

$$y\left(4y-89+33\right)=0$$

To find equation solutions, solve y=0 and 4y-56=0.

$$y=0 y=14$$

Steps Using the Quadratic Formula

Combine -89y and 33y to get -56y.

$$4y^{2}-56y=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, -56 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{-\left(-56\right)±\sqrt{\left(-56\right)^{2}}}{2\times 4}$$

Take the square root of \left(-56\right)^{2}.

$$y=\frac{-\left(-56\right)±56}{2\times 4}$$

The opposite of -56 is 56.

$$y=\frac{56±56}{2\times 4}$$

Multiply 2 times 4.

$$y=\frac{56±56}{8}$$

Now solve the equation y=\frac{56±56}{8} when ± is plus. Add 56 to 56.

$$y=\frac{112}{8}$$

Divide 112 by 8.

$$y=14$$

Now solve the equation y=\frac{56±56}{8} when ± is minus. Subtract 56 from 56.

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

Divide 0 by 8.

$$y=0$$

The equation is now solved.

$$y=14 y=0$$

Steps for Completing the Square

Combine -89y and 33y to get -56y.

$$4y^{2}-56y=0$$

Divide both sides by 4.

$$\frac{4y^{2}-56y}{4}=\frac{0}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$y^{2}+\left(-\frac{56}{4}\right)y=\frac{0}{4}$$

Divide -56 by 4.

$$y^{2}-14y=\frac{0}{4}$$

Divide 0 by 4.

$$y^{2}-14y=0$$

Divide -14, the coefficient of the x term, by 2 to get -7. Then add the square of -7 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$y^{2}-14y+\left(-7\right)^{2}=\left(-7\right)^{2}$$

Square -7.

$$y^{2}-14y+49=49$$

Factor y^{2}-14y+49. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

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

Take the square root of both sides of the equation.

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

Simplify.

$$y-7=7 y-7=-7$$

Add 7 to both sides of the equation.

$$y=14 y=0$$