Solve x^2=20110x

$$x ^ { 2 } = 20110 x$$

Solve for x

$$x=20110$$

$$x=0$$

Steps Using Factoring

Subtract 20110x from both sides.

$$x^{2}-20110x=0$$

Factor out x.

$$x\left(x-20110\right)=0$$

To find equation solutions, solve x=0 and x-20110=0.

$$x=0 x=20110$$

Steps Using the Quadratic Formula

Subtract 20110x from both sides.

$$x^{2}-20110x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -20110 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-20110\right)±\sqrt{\left(-20110\right)^{2}}}{2}$$

Take the square root of \left(-20110\right)^{2}.

$$x=\frac{-\left(-20110\right)±20110}{2}$$

The opposite of -20110 is 20110.

$$x=\frac{20110±20110}{2}$$

Now solve the equation x=\frac{20110±20110}{2} when ± is plus. Add 20110 to 20110.

$$x=\frac{40220}{2}$$

Divide 40220 by 2.

$$x=20110$$

Now solve the equation x=\frac{20110±20110}{2} when ± is minus. Subtract 20110 from 20110.

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

Divide 0 by 2.

$$x=0$$

The equation is now solved.

$$x=20110 x=0$$

Steps for Completing the Square

Subtract 20110x from both sides.

$$x^{2}-20110x=0$$

Divide -20110, the coefficient of the x term, by 2 to get -10055. Then add the square of -10055 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-20110x+\left(-10055\right)^{2}=\left(-10055\right)^{2}$$

Square -10055.

$$x^{2}-20110x+101103025=101103025$$

Factor x^{2}-20110x+101103025. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-10055\right)^{2}=101103025$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-10055\right)^{2}}=\sqrt{101103025}$$

Simplify.

$$x-10055=10055 x-10055=-10055$$

Add 10055 to both sides of the equation.

$$x=20110 x=0$$