Solve 2x(x-2)=8x^2-5x

$$2 x ( x - 2 ) = 8 x ^ { 2 } - 5 x$$

Solve for x

$$x=\frac{1}{6}\approx 0.166666667$$

$$x=0$$

Steps Using Factoring

Use the distributive property to multiply 2x by x-2.

$$2x^{2}-4x=8x^{2}-5x$$

Subtract 8x^{2} from both sides.

$$2x^{2}-4x-8x^{2}=-5x$$

Combine 2x^{2} and -8x^{2} to get -6x^{2}.

$$-6x^{2}-4x=-5x$$

Add 5x to both sides.

$$-6x^{2}-4x+5x=0$$

Combine -4x and 5x to get x.

$$-6x^{2}+x=0$$

Factor out x.

$$x\left(-6x+1\right)=0$$

To find equation solutions, solve x=0 and -6x+1=0.

$$x=0 x=\frac{1}{6}$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 2x by x-2.

$$2x^{2}-4x=8x^{2}-5x$$

Subtract 8x^{2} from both sides.

$$2x^{2}-4x-8x^{2}=-5x$$

Combine 2x^{2} and -8x^{2} to get -6x^{2}.

$$-6x^{2}-4x=-5x$$

Add 5x to both sides.

$$-6x^{2}-4x+5x=0$$

Combine -4x and 5x to get x.

$$-6x^{2}+x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -6 for a, 1 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Take the square root of 1^{2}.

$$x=\frac{-1±1}{2\left(-6\right)}$$

Multiply 2 times -6.

$$x=\frac{-1±1}{-12}$$

Now solve the equation x=\frac{-1±1}{-12} when ± is plus. Add -1 to 1.

$$x=\frac{0}{-12}$$

Divide 0 by -12.

$$x=0$$

Now solve the equation x=\frac{-1±1}{-12} when ± is minus. Subtract 1 from -1.

$$x=-\frac{2}{-12}$$

Reduce the fraction \frac{-2}{-12} to lowest terms by extracting and canceling out 2.

$$x=\frac{1}{6}$$

The equation is now solved.

$$x=0 x=\frac{1}{6}$$

Steps for Completing the Square

Use the distributive property to multiply 2x by x-2.

$$2x^{2}-4x=8x^{2}-5x$$

Subtract 8x^{2} from both sides.

$$2x^{2}-4x-8x^{2}=-5x$$

Combine 2x^{2} and -8x^{2} to get -6x^{2}.

$$-6x^{2}-4x=-5x$$

Add 5x to both sides.

$$-6x^{2}-4x+5x=0$$

Combine -4x and 5x to get x.

$$-6x^{2}+x=0$$

Divide both sides by -6.

$$\frac{-6x^{2}+x}{-6}=\frac{0}{-6}$$

Dividing by -6 undoes the multiplication by -6.

$$x^{2}+\frac{1}{-6}x=\frac{0}{-6}$$

Divide 1 by -6.

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

Divide 0 by -6.

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

Divide -\frac{1}{6}, the coefficient of the x term, by 2 to get -\frac{1}{12}. Then add the square of -\frac{1}{12} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{1}{6}x+\left(-\frac{1}{12}\right)^{2}=\left(-\frac{1}{12}\right)^{2}$$

Square -\frac{1}{12} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{1}{6}x+\frac{1}{144}=\frac{1}{144}$$

Factor x^{2}-\frac{1}{6}x+\frac{1}{144}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{1}{12}\right)^{2}=\frac{1}{144}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{1}{12}\right)^{2}}=\sqrt{\frac{1}{144}}$$

Simplify.

$$x-\frac{1}{12}=\frac{1}{12} x-\frac{1}{12}=-\frac{1}{12}$$

Add \frac{1}{12} to both sides of the equation.

$$x=\frac{1}{6} x=0$$