Solve 2x*6x=14x

$$2x \times 6x=14x$$

Solve for x

$$x = \frac{7}{6} = 1\frac{1}{6} \approx 1.166666667$$

$$x=0$$

Steps Using Factoring

Multiply x and x to get x^{2}.

$$2x^{2}\times 6=14x$$

Multiply 2 and 6 to get 12.

$$12x^{2}=14x$$

Subtract 14x from both sides.

$$12x^{2}-14x=0$$

Factor out x.

$$x\left(12x-14\right)=0$$

To find equation solutions, solve x=0 and 12x-14=0.

$$x=0 x=\frac{7}{6}$$

Steps Using the Quadratic Formula

Multiply x and x to get x^{2}.

$$2x^{2}\times 6=14x$$

Multiply 2 and 6 to get 12.

$$12x^{2}=14x$$

Subtract 14x from both sides.

$$12x^{2}-14x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 12 for a, -14 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-14\right)±\sqrt{\left(-14\right)^{2}}}{2\times 12}$$

Take the square root of \left(-14\right)^{2}.

$$x=\frac{-\left(-14\right)±14}{2\times 12}$$

The opposite of -14 is 14.

$$x=\frac{14±14}{2\times 12}$$

Multiply 2 times 12.

$$x=\frac{14±14}{24}$$

Now solve the equation x=\frac{14±14}{24} when ± is plus. Add 14 to 14.

$$x=\frac{28}{24}$$

Reduce the fraction \frac{28}{24} to lowest terms by extracting and canceling out 4.

$$x=\frac{7}{6}$$

Now solve the equation x=\frac{14±14}{24} when ± is minus. Subtract 14 from 14.

$$x=\frac{0}{24}$$

Divide 0 by 24.

$$x=0$$

The equation is now solved.

$$x=\frac{7}{6} x=0$$

Steps for Completing the Square

Multiply x and x to get x^{2}.

$$2x^{2}\times 6=14x$$

Multiply 2 and 6 to get 12.

$$12x^{2}=14x$$

Subtract 14x from both sides.

$$12x^{2}-14x=0$$

Divide both sides by 12.

$$\frac{12x^{2}-14x}{12}=\frac{0}{12}$$

Dividing by 12 undoes the multiplication by 12.

$$x^{2}+\left(-\frac{14}{12}\right)x=\frac{0}{12}$$

Reduce the fraction \frac{-14}{12} to lowest terms by extracting and canceling out 2.

$$x^{2}-\frac{7}{6}x=\frac{0}{12}$$

Divide 0 by 12.

$$x^{2}-\frac{7}{6}x=0$$

Divide -\frac{7}{6}, the coefficient of the x term, by 2 to get -\frac{7}{12}. Then add the square of -\frac{7}{12} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{7}{6}x+\left(-\frac{7}{12}\right)^{2}=\left(-\frac{7}{12}\right)^{2}$$

Square -\frac{7}{12} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{7}{6}x+\frac{49}{144}=\frac{49}{144}$$

Factor x^{2}-\frac{7}{6}x+\frac{49}{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}.

$$\left(x-\frac{7}{12}\right)^{2}=\frac{49}{144}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{7}{12}\right)^{2}}=\sqrt{\frac{49}{144}}$$

Simplify.

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

Add \frac{7}{12} to both sides of the equation.

$$x=\frac{7}{6} x=0$$