Solve 2x^2=14x

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

Solve for x

$$x=7$$

$$x=0$$

Steps Using Factoring

Subtract 14x from both sides.

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

Factor out x.

$$x\left(2x-14\right)=0$$

To find equation solutions, solve x=0 and 2x-14=0.

$$x=0 x=7$$

Steps Using the Quadratic Formula

Subtract 14x from both sides.

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

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

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

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

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

The opposite of -14 is 14.

$$x=\frac{14±14}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{14±14}{4}$$

Now solve the equation x=\frac{14±14}{4} when ± is plus. Add 14 to 14.

$$x=\frac{28}{4}$$

Divide 28 by 4.

$$x=7$$

Now solve the equation x=\frac{14±14}{4} when ± is minus. Subtract 14 from 14.

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

Divide 0 by 4.

$$x=0$$

The equation is now solved.

$$x=7 x=0$$

Steps for Completing the Square

Subtract 14x from both sides.

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

Divide both sides by 2.

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

Dividing by 2 undoes the multiplication by 2.

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

Divide -14 by 2.

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

Divide 0 by 2.

$$x^{2}-7x=0$$

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

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

Square -\frac{7}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-7x+\frac{49}{4}=\frac{49}{4}$$

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

$$\left(x-\frac{7}{2}\right)^{2}=\frac{49}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{7}{2}\right)^{2}}=\sqrt{\frac{49}{4}}$$

Simplify.

$$x-\frac{7}{2}=\frac{7}{2} x-\frac{7}{2}=-\frac{7}{2}$$

Add \frac{7}{2} to both sides of the equation.

$$x=7 x=0$$