Solve 0=y^2-14y

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

Solve for y

$$y=14$$

$$y=0$$

Steps Using Factoring

Swap sides so that all variable terms are on the left hand side.

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

Factor out y.

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

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

$$y=0 y=14$$

Steps Using the Quadratic Formula

Swap sides so that all variable terms are on the left hand side.

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

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}.

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

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

$$y=\frac{-\left(-14\right)±14}{2}$$

The opposite of -14 is 14.

$$y=\frac{14±14}{2}$$

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

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

Divide 28 by 2.

$$y=14$$

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

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

Divide 0 by 2.

$$y=0$$

The equation is now solved.

$$y=14 y=0$$

Steps for Completing the Square

Swap sides so that all variable terms are on the left hand side.

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

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.

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

Square -7.

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

Factor y^{2}-14y+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}.

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

Take the square root of both sides of the equation.

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

Simplify.

$$y-7=7 y-7=-7$$

Add 7 to both sides of the equation.

$$y=14 y=0$$