Solve =w(w+5)=0

$$= w ( w + 5 ) = 0$$

Solve for w

$$w=-5$$

$$w=0$$

Steps Using Factoring

Use the distributive property to multiply w by w+5.

$$w^{2}+5w=0$$

Factor out w.

$$w\left(w+5\right)=0$$

To find equation solutions, solve w=0 and w+5=0.

$$w=0 w=-5$$

Steps Using the Quadratic Formula

Use the distributive property to multiply w by w+5.

$$w^{2}+5w=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 5 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$w=\frac{-5±\sqrt{5^{2}}}{2}$$

Take the square root of 5^{2}.

$$w=\frac{-5±5}{2}$$

Now solve the equation w=\frac{-5±5}{2} when ± is plus. Add -5 to 5.

$$w=\frac{0}{2}$$

Divide 0 by 2.

$$w=0$$

Now solve the equation w=\frac{-5±5}{2} when ± is minus. Subtract 5 from -5.

$$w=-\frac{10}{2}$$

Divide -10 by 2.

$$w=-5$$

The equation is now solved.

$$w=0 w=-5$$

Steps for Completing the Square

Use the distributive property to multiply w by w+5.

$$w^{2}+5w=0$$

Divide 5, the coefficient of the x term, by 2 to get \frac{5}{2}. Then add the square of \frac{5}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$w^{2}+5w+\left(\frac{5}{2}\right)^{2}=\left(\frac{5}{2}\right)^{2}$$

Square \frac{5}{2} by squaring both the numerator and the denominator of the fraction.

$$w^{2}+5w+\frac{25}{4}=\frac{25}{4}$$

Factor w^{2}+5w+\frac{25}{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}.

$$\left(w+\frac{5}{2}\right)^{2}=\frac{25}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(w+\frac{5}{2}\right)^{2}}=\sqrt{\frac{25}{4}}$$

Simplify.

$$w+\frac{5}{2}=\frac{5}{2} w+\frac{5}{2}=-\frac{5}{2}$$

Subtract \frac{5}{2} from both sides of the equation.

$$w=0 w=-5$$