Solve 4w^2=-24w

$$4 w ^ { 2 } = - 24 w$$

Solve for w

$$w=-6$$

$$w=0$$

Steps Using Factoring

Add 24w to both sides.

$$4w^{2}+24w=0$$

Factor out w.

$$w\left(4w+24\right)=0$$

To find equation solutions, solve w=0 and 4w+24=0.

$$w=0 w=-6$$

Steps Using the Quadratic Formula

Add 24w to both sides.

$$4w^{2}+24w=0$$

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}.

$$w=\frac{-24±\sqrt{24^{2}}}{2\times 4}$$

Take the square root of 24^{2}.

$$w=\frac{-24±24}{2\times 4}$$

Multiply 2 times 4.

$$w=\frac{-24±24}{8}$$

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

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

Divide 0 by 8.

$$w=0$$

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

$$w=-\frac{48}{8}$$

Divide -48 by 8.

$$w=-6$$

The equation is now solved.

$$w=0 w=-6$$

Steps for Completing the Square

Add 24w to both sides.

$$4w^{2}+24w=0$$

Divide both sides by 4.

$$\frac{4w^{2}+24w}{4}=\frac{0}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$w^{2}+\frac{24}{4}w=\frac{0}{4}$$

Divide 24 by 4.

$$w^{2}+6w=\frac{0}{4}$$

Divide 0 by 4.

$$w^{2}+6w=0$$

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.

$$w^{2}+6w+3^{2}=3^{2}$$

Square 3.

$$w^{2}+6w+9=9$$

Factor w^{2}+6w+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}.

$$\left(w+3\right)^{2}=9$$

Take the square root of both sides of the equation.

$$\sqrt{\left(w+3\right)^{2}}=\sqrt{9}$$

Simplify.

$$w+3=3 w+3=-3$$

Subtract 3 from both sides of the equation.

$$w=0 w=-6$$