Solve w-w=w+w*w

$$w - w = w + w \times w$$

Solve for w

$$w=-1$$

$$w=0$$

Steps Using Factoring

Multiply w and w to get w^{2}.

$$w-w=w+w^{2}$$

Combine w and -w to get 0.

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

Swap sides so that all variable terms are on the left hand side.

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

Factor out w.

$$w\left(1+w\right)=0$$

To find equation solutions, solve w=0 and 1+w=0.

$$w=0 w=-1$$

Steps Using the Quadratic Formula

Multiply w and w to get w^{2}.

$$w-w=w+w^{2}$$

Combine w and -w to get 0.

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

Swap sides so that all variable terms are on the left hand side.

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

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

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

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

$$w=\frac{-1±\sqrt{1^{2}}}{2}$$

Take the square root of 1^{2}.

$$w=\frac{-1±1}{2}$$

Now solve the equation w=\frac{-1±1}{2} when ± is plus. Add -1 to 1.

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

Divide 0 by 2.

$$w=0$$

Now solve the equation w=\frac{-1±1}{2} when ± is minus. Subtract 1 from -1.

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

Divide -2 by 2.

$$w=-1$$

The equation is now solved.

$$w=0 w=-1$$

Steps for Completing the Square

Multiply w and w to get w^{2}.

$$w-w=w+w^{2}$$

Combine w and -w to get 0.

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

Swap sides so that all variable terms are on the left hand side.

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

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

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

Divide 1, the coefficient of the x term, by 2 to get \frac{1}{2}. Then add the square of \frac{1}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$w^{2}+w+\left(\frac{1}{2}\right)^{2}=\left(\frac{1}{2}\right)^{2}$$

Square \frac{1}{2} by squaring both the numerator and the denominator of the fraction.

$$w^{2}+w+\frac{1}{4}=\frac{1}{4}$$

Factor w^{2}+w+\frac{1}{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}.

$$\left(w+\frac{1}{2}\right)^{2}=\frac{1}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(w+\frac{1}{2}\right)^{2}}=\sqrt{\frac{1}{4}}$$

Simplify.

$$w+\frac{1}{2}=\frac{1}{2} w+\frac{1}{2}=-\frac{1}{2}$$

Subtract \frac{1}{2} from both sides of the equation.

$$w=0 w=-1$$