Solve 5x^2=10x

$$5 { x }^{ 2 } =10x$$

Solve for x

$$x=2$$

$$x=0$$

Steps Using Factoring

Subtract 10x from both sides.

$$5x^{2}-10x=0$$

Factor out x.

$$x\left(5x-10\right)=0$$

To find equation solutions, solve x=0 and 5x-10=0.

$$x=0 x=2$$

Steps Using the Quadratic Formula

Subtract 10x from both sides.

$$5x^{2}-10x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, -10 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}}}{2\times 5}$$

Take the square root of \left(-10\right)^{2}.

$$x=\frac{-\left(-10\right)±10}{2\times 5}$$

The opposite of -10 is 10.

$$x=\frac{10±10}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{10±10}{10}$$

Now solve the equation x=\frac{10±10}{10} when ± is plus. Add 10 to 10.

$$x=\frac{20}{10}$$

Divide 20 by 10.

$$x=2$$

Now solve the equation x=\frac{10±10}{10} when ± is minus. Subtract 10 from 10.

$$x=\frac{0}{10}$$

Divide 0 by 10.

$$x=0$$

The equation is now solved.

$$x=2 x=0$$

Steps for Completing the Square

Subtract 10x from both sides.

$$5x^{2}-10x=0$$

Divide both sides by 5.

$$\frac{5x^{2}-10x}{5}=\frac{0}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$x^{2}+\left(-\frac{10}{5}\right)x=\frac{0}{5}$$

Divide -10 by 5.

$$x^{2}-2x=\frac{0}{5}$$

Divide 0 by 5.

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

Divide -2, the coefficient of the x term, by 2 to get -1. Then add the square of -1 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-2x+1=1$$

Factor x^{2}-2x+1. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-1\right)^{2}=1$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-1\right)^{2}}=\sqrt{1}$$

Simplify.

$$x-1=1 x-1=-1$$

Add 1 to both sides of the equation.

$$x=2 x=0$$