Solve y^2=-14y

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

Solve for y

$$y=-14$$

$$y=0$$

Steps Using Factoring

Add 14y to both sides.

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

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

Add 14y to both sides.

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

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}.

$$y=\frac{-14±\sqrt{14^{2}}}{2}$$

Take the square root of 14^{2}.

$$y=\frac{-14±14}{2}$$

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

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

Divide 0 by 2.

$$y=0$$

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

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

Divide -28 by 2.

$$y=-14$$

The equation is now solved.

$$y=0 y=-14$$

Steps for Completing the Square

Add 14y to both sides.

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

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.

$$y^{2}+14y+7^{2}=7^{2}$$

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.

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

Subtract 7 from both sides of the equation.

$$y=0 y=-14$$