Solve x^2=25x

$$x ^ { 2 } = 25 x$$

Solve for x

$$x=25$$

$$x=0$$

Steps Using Factoring

Subtract 25x from both sides.

$$x^{2}-25x=0$$

Factor out x.

$$x\left(x-25\right)=0$$

To find equation solutions, solve x=0 and x-25=0.

$$x=0 x=25$$

Steps Using the Quadratic Formula

Subtract 25x from both sides.

$$x^{2}-25x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -25 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-25\right)±\sqrt{\left(-25\right)^{2}}}{2}$$

Take the square root of \left(-25\right)^{2}.

$$x=\frac{-\left(-25\right)±25}{2}$$

The opposite of -25 is 25.

$$x=\frac{25±25}{2}$$

Now solve the equation x=\frac{25±25}{2} when ± is plus. Add 25 to 25.

$$x=\frac{50}{2}$$

Divide 50 by 2.

$$x=25$$

Now solve the equation x=\frac{25±25}{2} when ± is minus. Subtract 25 from 25.

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

Divide 0 by 2.

$$x=0$$

The equation is now solved.

$$x=25 x=0$$

Steps for Completing the Square

Subtract 25x from both sides.

$$x^{2}-25x=0$$

Divide -25, the coefficient of the x term, by 2 to get -\frac{25}{2}. Then add the square of -\frac{25}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-25x+\left(-\frac{25}{2}\right)^{2}=\left(-\frac{25}{2}\right)^{2}$$

Square -\frac{25}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-25x+\frac{625}{4}=\frac{625}{4}$$

Factor x^{2}-25x+\frac{625}{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}.

$$\left(x-\frac{25}{2}\right)^{2}=\frac{625}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{25}{2}\right)^{2}}=\sqrt{\frac{625}{4}}$$

Simplify.

$$x-\frac{25}{2}=\frac{25}{2} x-\frac{25}{2}=-\frac{25}{2}$$

Add \frac{25}{2} to both sides of the equation.

$$x=25 x=0$$