Solve x^2=28x

$$x ^ { 2 } = 28 x$$

Solve for x

$$x=28$$

$$x=0$$

Steps Using Factoring

Subtract 28x from both sides.

$$x^{2}-28x=0$$

Factor out x.

$$x\left(x-28\right)=0$$

To find equation solutions, solve x=0 and x-28=0.

$$x=0 x=28$$

Steps Using the Quadratic Formula

Subtract 28x from both sides.

$$x^{2}-28x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -28 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-28\right)±\sqrt{\left(-28\right)^{2}}}{2}$$

Take the square root of \left(-28\right)^{2}.

$$x=\frac{-\left(-28\right)±28}{2}$$

The opposite of -28 is 28.

$$x=\frac{28±28}{2}$$

Now solve the equation x=\frac{28±28}{2} when ± is plus. Add 28 to 28.

$$x=\frac{56}{2}$$

Divide 56 by 2.

$$x=28$$

Now solve the equation x=\frac{28±28}{2} when ± is minus. Subtract 28 from 28.

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

Divide 0 by 2.

$$x=0$$

The equation is now solved.

$$x=28 x=0$$

Steps for Completing the Square

Subtract 28x from both sides.

$$x^{2}-28x=0$$

Divide -28, the coefficient of the x term, by 2 to get -14. Then add the square of -14 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-28x+\left(-14\right)^{2}=\left(-14\right)^{2}$$

Square -14.

$$x^{2}-28x+196=196$$

Factor x^{2}-28x+196. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-14\right)^{2}=196$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-14\right)^{2}}=\sqrt{196}$$

Simplify.

$$x-14=14 x-14=-14$$

Add 14 to both sides of the equation.

$$x=28 x=0$$