Solve 5x^2=210x

$$5 x ^ { 2 } = 210 x$$

Solve for x

$$x=42$$

$$x=0$$

Steps Using Factoring

Subtract 210x from both sides.

$$5x^{2}-210x=0$$

Factor out x.

$$x\left(5x-210\right)=0$$

To find equation solutions, solve x=0 and 5x-210=0.

$$x=0 x=42$$

Steps Using the Quadratic Formula

Subtract 210x from both sides.

$$5x^{2}-210x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, -210 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-210\right)±\sqrt{\left(-210\right)^{2}}}{2\times 5}$$

Take the square root of \left(-210\right)^{2}.

$$x=\frac{-\left(-210\right)±210}{2\times 5}$$

The opposite of -210 is 210.

$$x=\frac{210±210}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{210±210}{10}$$

Now solve the equation x=\frac{210±210}{10} when ± is plus. Add 210 to 210.

$$x=\frac{420}{10}$$

Divide 420 by 10.

$$x=42$$

Now solve the equation x=\frac{210±210}{10} when ± is minus. Subtract 210 from 210.

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

Divide 0 by 10.

$$x=0$$

The equation is now solved.

$$x=42 x=0$$

Steps for Completing the Square

Subtract 210x from both sides.

$$5x^{2}-210x=0$$

Divide both sides by 5.

$$\frac{5x^{2}-210x}{5}=\frac{0}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$x^{2}+\left(-\frac{210}{5}\right)x=\frac{0}{5}$$

Divide -210 by 5.

$$x^{2}-42x=\frac{0}{5}$$

Divide 0 by 5.

$$x^{2}-42x=0$$

Divide -42, the coefficient of the x term, by 2 to get -21. Then add the square of -21 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-42x+\left(-21\right)^{2}=\left(-21\right)^{2}$$

Square -21.

$$x^{2}-42x+441=441$$

Factor x^{2}-42x+441. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-21\right)^{2}=441$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-21\right)^{2}}=\sqrt{441}$$

Simplify.

$$x-21=21 x-21=-21$$

Add 21 to both sides of the equation.

$$x=42 x=0$$