Solve x^2=30x

$$x ^ { 2 } = 30 x$$

Solve for x

$$x=30$$

$$x=0$$

Steps Using Factoring

Subtract 30x from both sides.

$$x^{2}-30x=0$$

Factor out x.

$$x\left(x-30\right)=0$$

To find equation solutions, solve x=0 and x-30=0.

$$x=0 x=30$$

Steps Using the Quadratic Formula

Subtract 30x from both sides.

$$x^{2}-30x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -30 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-30\right)±\sqrt{\left(-30\right)^{2}}}{2}$$

Take the square root of \left(-30\right)^{2}.

$$x=\frac{-\left(-30\right)±30}{2}$$

The opposite of -30 is 30.

$$x=\frac{30±30}{2}$$

Now solve the equation x=\frac{30±30}{2} when ± is plus. Add 30 to 30.

$$x=\frac{60}{2}$$

Divide 60 by 2.

$$x=30$$

Now solve the equation x=\frac{30±30}{2} when ± is minus. Subtract 30 from 30.

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

Divide 0 by 2.

$$x=0$$

The equation is now solved.

$$x=30 x=0$$

Steps for Completing the Square

Subtract 30x from both sides.

$$x^{2}-30x=0$$

Divide -30, the coefficient of the x term, by 2 to get -15. Then add the square of -15 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-30x+\left(-15\right)^{2}=\left(-15\right)^{2}$$

Square -15.

$$x^{2}-30x+225=225$$

Factor x^{2}-30x+225. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-15\right)^{2}=225$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-15\right)^{2}}=\sqrt{225}$$

Simplify.

$$x-15=15 x-15=-15$$

Add 15 to both sides of the equation.

$$x=30 x=0$$