Solve x(-6x-2)4=-22x

$$x ( - 6 x - 2 ) 4 = - 22 x$$

Solve for x

$$x=\frac{7}{12}\approx 0.583333333$$

$$x=0$$

Steps Using Factoring

Use the distributive property to multiply x by -6x-2.

$$\left(-6x^{2}-2x\right)\times 4=-22x$$

Use the distributive property to multiply -6x^{2}-2x by 4.

$$-24x^{2}-8x=-22x$$

Add 22x to both sides.

$$-24x^{2}-8x+22x=0$$

Combine -8x and 22x to get 14x.

$$-24x^{2}+14x=0$$

Factor out x.

$$x\left(-24x+14\right)=0$$

To find equation solutions, solve x=0 and -24x+14=0.

$$x=0 x=\frac{7}{12}$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x by -6x-2.

$$\left(-6x^{2}-2x\right)\times 4=-22x$$

Use the distributive property to multiply -6x^{2}-2x by 4.

$$-24x^{2}-8x=-22x$$

Add 22x to both sides.

$$-24x^{2}-8x+22x=0$$

Combine -8x and 22x to get 14x.

$$-24x^{2}+14x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -24 for a, 14 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-14±\sqrt{14^{2}}}{2\left(-24\right)}$$

Take the square root of 14^{2}.

$$x=\frac{-14±14}{2\left(-24\right)}$$

Multiply 2 times -24.

$$x=\frac{-14±14}{-48}$$

Now solve the equation x=\frac{-14±14}{-48} when ± is plus. Add -14 to 14.

$$x=\frac{0}{-48}$$

Divide 0 by -48.

$$x=0$$

Now solve the equation x=\frac{-14±14}{-48} when ± is minus. Subtract 14 from -14.

$$x=-\frac{28}{-48}$$

Reduce the fraction \frac{-28}{-48} to lowest terms by extracting and canceling out 4.

$$x=\frac{7}{12}$$

The equation is now solved.

$$x=0 x=\frac{7}{12}$$

Steps for Completing the Square

Use the distributive property to multiply x by -6x-2.

$$\left(-6x^{2}-2x\right)\times 4=-22x$$

Use the distributive property to multiply -6x^{2}-2x by 4.

$$-24x^{2}-8x=-22x$$

Add 22x to both sides.

$$-24x^{2}-8x+22x=0$$

Combine -8x and 22x to get 14x.

$$-24x^{2}+14x=0$$

Divide both sides by -24.

$$\frac{-24x^{2}+14x}{-24}=\frac{0}{-24}$$

Dividing by -24 undoes the multiplication by -24.

$$x^{2}+\frac{14}{-24}x=\frac{0}{-24}$$

Reduce the fraction \frac{14}{-24} to lowest terms by extracting and canceling out 2.

$$x^{2}-\frac{7}{12}x=\frac{0}{-24}$$

Divide 0 by -24.

$$x^{2}-\frac{7}{12}x=0$$

Divide -\frac{7}{12}, the coefficient of the x term, by 2 to get -\frac{7}{24}. Then add the square of -\frac{7}{24} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{7}{12}x+\left(-\frac{7}{24}\right)^{2}=\left(-\frac{7}{24}\right)^{2}$$

Square -\frac{7}{24} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{7}{12}x+\frac{49}{576}=\frac{49}{576}$$

Factor x^{2}-\frac{7}{12}x+\frac{49}{576}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{7}{24}\right)^{2}=\frac{49}{576}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{7}{24}\right)^{2}}=\sqrt{\frac{49}{576}}$$

Simplify.

$$x-\frac{7}{24}=\frac{7}{24} x-\frac{7}{24}=-\frac{7}{24}$$

Add \frac{7}{24} to both sides of the equation.

$$x=\frac{7}{12} x=0$$