Solve 10x^2=80x

$$10 { x }^{ 2 } =80x$$

Solve for x

$$x=8$$

$$x=0$$

Steps Using Factoring

Subtract 80x from both sides.

$$10x^{2}-80x=0$$

Factor out x.

$$x\left(10x-80\right)=0$$

To find equation solutions, solve x=0 and 10x-80=0.

$$x=0 x=8$$

Steps Using the Quadratic Formula

Subtract 80x from both sides.

$$10x^{2}-80x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 10 for a, -80 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-80\right)±\sqrt{\left(-80\right)^{2}}}{2\times 10}$$

Take the square root of \left(-80\right)^{2}.

$$x=\frac{-\left(-80\right)±80}{2\times 10}$$

The opposite of -80 is 80.

$$x=\frac{80±80}{2\times 10}$$

Multiply 2 times 10.

$$x=\frac{80±80}{20}$$

Now solve the equation x=\frac{80±80}{20} when ± is plus. Add 80 to 80.

$$x=\frac{160}{20}$$

Divide 160 by 20.

$$x=8$$

Now solve the equation x=\frac{80±80}{20} when ± is minus. Subtract 80 from 80.

$$x=\frac{0}{20}$$

Divide 0 by 20.

$$x=0$$

The equation is now solved.

$$x=8 x=0$$

Steps for Completing the Square

Subtract 80x from both sides.

$$10x^{2}-80x=0$$

Divide both sides by 10.

$$\frac{10x^{2}-80x}{10}=\frac{0}{10}$$

Dividing by 10 undoes the multiplication by 10.

$$x^{2}+\left(-\frac{80}{10}\right)x=\frac{0}{10}$$

Divide -80 by 10.

$$x^{2}-8x=\frac{0}{10}$$

Divide 0 by 10.

$$x^{2}-8x=0$$

Divide -8, the coefficient of the x term, by 2 to get -4. Then add the square of -4 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-8x+\left(-4\right)^{2}=\left(-4\right)^{2}$$

Square -4.

$$x^{2}-8x+16=16$$

Factor x^{2}-8x+16. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-4\right)^{2}=16$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-4\right)^{2}}=\sqrt{16}$$

Simplify.

$$x-4=4 x-4=-4$$

Add 4 to both sides of the equation.

$$x=8 x=0$$