Solve a^2=11a

$$a ^ { 2 } = 11 a$$

Solve for a

$$a=11$$

$$a=0$$

Steps Using Factoring

Subtract 11a from both sides.

$$a^{2}-11a=0$$

Factor out a.

$$a\left(a-11\right)=0$$

To find equation solutions, solve a=0 and a-11=0.

$$a=0 a=11$$

Steps Using the Quadratic Formula

Subtract 11a from both sides.

$$a^{2}-11a=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -11 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{-\left(-11\right)±\sqrt{\left(-11\right)^{2}}}{2}$$

Take the square root of \left(-11\right)^{2}.

$$a=\frac{-\left(-11\right)±11}{2}$$

The opposite of -11 is 11.

$$a=\frac{11±11}{2}$$

Now solve the equation a=\frac{11±11}{2} when ± is plus. Add 11 to 11.

$$a=\frac{22}{2}$$

Divide 22 by 2.

$$a=11$$

Now solve the equation a=\frac{11±11}{2} when ± is minus. Subtract 11 from 11.

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

Divide 0 by 2.

$$a=0$$

The equation is now solved.

$$a=11 a=0$$

Steps for Completing the Square

Subtract 11a from both sides.

$$a^{2}-11a=0$$

Divide -11, the coefficient of the x term, by 2 to get -\frac{11}{2}. Then add the square of -\frac{11}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$a^{2}-11a+\left(-\frac{11}{2}\right)^{2}=\left(-\frac{11}{2}\right)^{2}$$

Square -\frac{11}{2} by squaring both the numerator and the denominator of the fraction.

$$a^{2}-11a+\frac{121}{4}=\frac{121}{4}$$

Factor a^{2}-11a+\frac{121}{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}.

$$\left(a-\frac{11}{2}\right)^{2}=\frac{121}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(a-\frac{11}{2}\right)^{2}}=\sqrt{\frac{121}{4}}$$

Simplify.

$$a-\frac{11}{2}=\frac{11}{2} a-\frac{11}{2}=-\frac{11}{2}$$

Add \frac{11}{2} to both sides of the equation.

$$a=11 a=0$$