Solve 8x(x-9)=0

$$8 x ( x - 9 ) = 0$$

Solve for x

$$x=9$$

$$x=0$$

Steps Using Factoring

Use the distributive property to multiply 8x by x-9.

$$8x^{2}-72x=0$$

Factor out x.

$$x\left(8x-72\right)=0$$

To find equation solutions, solve x=0 and 8x-72=0.

$$x=0 x=9$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 8x by x-9.

$$8x^{2}-72x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, -72 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-72\right)±\sqrt{\left(-72\right)^{2}}}{2\times 8}$$

Take the square root of \left(-72\right)^{2}.

$$x=\frac{-\left(-72\right)±72}{2\times 8}$$

The opposite of -72 is 72.

$$x=\frac{72±72}{2\times 8}$$

Multiply 2 times 8.

$$x=\frac{72±72}{16}$$

Now solve the equation x=\frac{72±72}{16} when ± is plus. Add 72 to 72.

$$x=\frac{144}{16}$$

Divide 144 by 16.

$$x=9$$

Now solve the equation x=\frac{72±72}{16} when ± is minus. Subtract 72 from 72.

$$x=\frac{0}{16}$$

Divide 0 by 16.

$$x=0$$

The equation is now solved.

$$x=9 x=0$$

Steps for Completing the Square

Use the distributive property to multiply 8x by x-9.

$$8x^{2}-72x=0$$

Divide both sides by 8.

$$\frac{8x^{2}-72x}{8}=\frac{0}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$x^{2}+\left(-\frac{72}{8}\right)x=\frac{0}{8}$$

Divide -72 by 8.

$$x^{2}-9x=\frac{0}{8}$$

Divide 0 by 8.

$$x^{2}-9x=0$$

Divide -9, the coefficient of the x term, by 2 to get -\frac{9}{2}. Then add the square of -\frac{9}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-9x+\left(-\frac{9}{2}\right)^{2}=\left(-\frac{9}{2}\right)^{2}$$

Square -\frac{9}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-9x+\frac{81}{4}=\frac{81}{4}$$

Factor x^{2}-9x+\frac{81}{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}.

$$\left(x-\frac{9}{2}\right)^{2}=\frac{81}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{9}{2}\right)^{2}}=\sqrt{\frac{81}{4}}$$

Simplify.

$$x-\frac{9}{2}=\frac{9}{2} x-\frac{9}{2}=-\frac{9}{2}$$

Add \frac{9}{2} to both sides of the equation.

$$x=9 x=0$$