Solve left(-xright)^2-14x=0

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

Solve for x

$$x=14$$

$$x=0$$

Steps Using Factoring

Calculate -x to the power of 2 and get x^{2}.

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

Factor out x.

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

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

$$x=0 x=14$$

Steps Using the Quadratic Formula

Calculate -x to the power of 2 and get x^{2}.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -14 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

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

$$x=\frac{-\left(-14\right)±14}{2}$$

The opposite of -14 is 14.

$$x=\frac{14±14}{2}$$

Now solve the equation x=\frac{14±14}{2} when ± is plus. Add 14 to 14.

$$x=\frac{28}{2}$$

Divide 28 by 2.

$$x=14$$

Now solve the equation x=\frac{14±14}{2} when ± is minus. Subtract 14 from 14.

$$x=\frac{0}{2}$$

Divide 0 by 2.

$$x=0$$

The equation is now solved.

$$x=14 x=0$$

Steps for Completing the Square

Calculate -x to the power of 2 and get x^{2}.

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

Divide -14, the coefficient of the x term, by 2 to get -7. Then add the square of -7 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-14x+\left(-7\right)^{2}=\left(-7\right)^{2}$$

Square -7.

$$x^{2}-14x+49=49$$

Factor x^{2}-14x+49. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

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

Take the square root of both sides of the equation.

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

Simplify.

$$x-7=7 x-7=-7$$

Add 7 to both sides of the equation.

$$x=14 x=0$$