Solve 0.125x^2-1/2x(x-6)=0

$$0.125 x ^ { 2 } - \frac { 1 } { 2 } x ( x - 6 ) = 0$$

Solve for x

$$x=8$$

$$x=0$$

Steps Using Factoring

Multiply -1 and \frac{1}{2} to get -\frac{1}{2}.

$$0.125x^{2}-\frac{1}{2}x\left(x-6\right)=0$$

Use the distributive property to multiply -\frac{1}{2}x by x-6.

$$0.125x^{2}-\frac{1}{2}x^{2}+3x=0$$

Combine 0.125x^{2} and -\frac{1}{2}x^{2} to get -\frac{3}{8}x^{2}.

$$-\frac{3}{8}x^{2}+3x=0$$

Factor out x.

$$x\left(-\frac{3}{8}x+3\right)=0$$

To find equation solutions, solve x=0 and -\frac{3x}{8}+3=0.

$$x=0 x=8$$

Steps Using the Quadratic Formula

Multiply -1 and \frac{1}{2} to get -\frac{1}{2}.

$$0.125x^{2}-\frac{1}{2}x\left(x-6\right)=0$$

Use the distributive property to multiply -\frac{1}{2}x by x-6.

$$0.125x^{2}-\frac{1}{2}x^{2}+3x=0$$

Combine 0.125x^{2} and -\frac{1}{2}x^{2} to get -\frac{3}{8}x^{2}.

$$-\frac{3}{8}x^{2}+3x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -\frac{3}{8} for a, 3 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-3±\sqrt{3^{2}}}{2\left(-\frac{3}{8}\right)}$$

Take the square root of 3^{2}.

$$x=\frac{-3±3}{2\left(-\frac{3}{8}\right)}$$

Multiply 2 times -\frac{3}{8}.

$$x=\frac{-3±3}{-\frac{3}{4}}$$

Now solve the equation x=\frac{-3±3}{-\frac{3}{4}} when ± is plus. Add -3 to 3.

$$x=\frac{0}{-\frac{3}{4}}$$

Divide 0 by -\frac{3}{4} by multiplying 0 by the reciprocal of -\frac{3}{4}.

$$x=0$$

Now solve the equation x=\frac{-3±3}{-\frac{3}{4}} when ± is minus. Subtract 3 from -3.

$$x=-\frac{6}{-\frac{3}{4}}$$

Divide -6 by -\frac{3}{4} by multiplying -6 by the reciprocal of -\frac{3}{4}.

$$x=8$$

The equation is now solved.

$$x=0 x=8$$

Steps for Completing the Square

Multiply -1 and \frac{1}{2} to get -\frac{1}{2}.

$$0.125x^{2}-\frac{1}{2}x\left(x-6\right)=0$$

Use the distributive property to multiply -\frac{1}{2}x by x-6.

$$0.125x^{2}-\frac{1}{2}x^{2}+3x=0$$

Combine 0.125x^{2} and -\frac{1}{2}x^{2} to get -\frac{3}{8}x^{2}.

$$-\frac{3}{8}x^{2}+3x=0$$

Divide both sides of the equation by -\frac{3}{8}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-\frac{3}{8}x^{2}+3x}{-\frac{3}{8}}=\frac{0}{-\frac{3}{8}}$$

Dividing by -\frac{3}{8} undoes the multiplication by -\frac{3}{8}.

$$x^{2}+\frac{3}{-\frac{3}{8}}x=\frac{0}{-\frac{3}{8}}$$

Divide 3 by -\frac{3}{8} by multiplying 3 by the reciprocal of -\frac{3}{8}.

$$x^{2}-8x=\frac{0}{-\frac{3}{8}}$$

Divide 0 by -\frac{3}{8} by multiplying 0 by the reciprocal of -\frac{3}{8}.

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

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.

$$x=8 x=0$$