Solve a^2+3a-2a=0

$${ a }^{ 2 } +3a-2a=0$$

Solve for a

$$a=-1$$

$$a=0$$

Steps Using Factoring

Factor out a.

$$a\left(a+3-2\right)=0$$

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

$$a=0 a=-1$$

Steps Using the Quadratic Formula

Combine 3a and -2a to get a.

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

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}.

$$a=\frac{-1±\sqrt{1^{2}}}{2}$$

Take the square root of 1^{2}.

$$a=\frac{-1±1}{2}$$

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

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

Divide 0 by 2.

$$a=0$$

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

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

Divide -2 by 2.

$$a=-1$$

The equation is now solved.

$$a=0 a=-1$$

Steps for Completing the Square

Combine 3a and -2a to get a.

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

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.

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

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

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

Factor a^{2}+a+\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}.

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

Take the square root of both sides of the equation.

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

Simplify.

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

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

$$a=0 a=-1$$