Solve 4q^2-28q=-4q

$$4 q ^ { 2 } - 28 q = - 4 q$$

Solve for q

$$q=6$$

$$q=0$$

Steps Using Factoring

Add 4q to both sides.

$$4q^{2}-28q+4q=0$$

Combine -28q and 4q to get -24q.

$$4q^{2}-24q=0$$

Factor out q.

$$q\left(4q-24\right)=0$$

To find equation solutions, solve q=0 and 4q-24=0.

$$q=0 q=6$$

Steps Using the Quadratic Formula

Add 4q to both sides.

$$4q^{2}-28q+4q=0$$

Combine -28q and 4q to get -24q.

$$4q^{2}-24q=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, -24 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$q=\frac{-\left(-24\right)±\sqrt{\left(-24\right)^{2}}}{2\times 4}$$

Take the square root of \left(-24\right)^{2}.

$$q=\frac{-\left(-24\right)±24}{2\times 4}$$

The opposite of -24 is 24.

$$q=\frac{24±24}{2\times 4}$$

Multiply 2 times 4.

$$q=\frac{24±24}{8}$$

Now solve the equation q=\frac{24±24}{8} when ± is plus. Add 24 to 24.

$$q=\frac{48}{8}$$

Divide 48 by 8.

$$q=6$$

Now solve the equation q=\frac{24±24}{8} when ± is minus. Subtract 24 from 24.

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

Divide 0 by 8.

$$q=0$$

The equation is now solved.

$$q=6 q=0$$

Steps for Completing the Square

Add 4q to both sides.

$$4q^{2}-28q+4q=0$$

Combine -28q and 4q to get -24q.

$$4q^{2}-24q=0$$

Divide both sides by 4.

$$\frac{4q^{2}-24q}{4}=\frac{0}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$q^{2}+\left(-\frac{24}{4}\right)q=\frac{0}{4}$$

Divide -24 by 4.

$$q^{2}-6q=\frac{0}{4}$$

Divide 0 by 4.

$$q^{2}-6q=0$$

Divide -6, the coefficient of the x term, by 2 to get -3. Then add the square of -3 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$q^{2}-6q+\left(-3\right)^{2}=\left(-3\right)^{2}$$

Square -3.

$$q^{2}-6q+9=9$$

Factor q^{2}-6q+9. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(q-3\right)^{2}=9$$

Take the square root of both sides of the equation.

$$\sqrt{\left(q-3\right)^{2}}=\sqrt{9}$$

Simplify.

$$q-3=3 q-3=-3$$

Add 3 to both sides of the equation.

$$q=6 q=0$$