Solve y^2=-13y

$$y ^ { 2 } = - 13 y$$

Solve for y

$$y=-13$$

$$y=0$$

Steps Using Factoring

Add 13y to both sides.

$$y^{2}+13y=0$$

Factor out y.

$$y\left(y+13\right)=0$$

To find equation solutions, solve y=0 and y+13=0.

$$y=0 y=-13$$

Steps Using the Quadratic Formula

Add 13y to both sides.

$$y^{2}+13y=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 13 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{-13±\sqrt{13^{2}}}{2}$$

Take the square root of 13^{2}.

$$y=\frac{-13±13}{2}$$

Now solve the equation y=\frac{-13±13}{2} when ± is plus. Add -13 to 13.

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

Divide 0 by 2.

$$y=0$$

Now solve the equation y=\frac{-13±13}{2} when ± is minus. Subtract 13 from -13.

$$y=-\frac{26}{2}$$

Divide -26 by 2.

$$y=-13$$

The equation is now solved.

$$y=0 y=-13$$

Steps for Completing the Square

Add 13y to both sides.

$$y^{2}+13y=0$$

Divide 13, the coefficient of the x term, by 2 to get \frac{13}{2}. Then add the square of \frac{13}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$y^{2}+13y+\left(\frac{13}{2}\right)^{2}=\left(\frac{13}{2}\right)^{2}$$

Square \frac{13}{2} by squaring both the numerator and the denominator of the fraction.

$$y^{2}+13y+\frac{169}{4}=\frac{169}{4}$$

Factor y^{2}+13y+\frac{169}{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}.

$$\left(y+\frac{13}{2}\right)^{2}=\frac{169}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(y+\frac{13}{2}\right)^{2}}=\sqrt{\frac{169}{4}}$$

Simplify.

$$y+\frac{13}{2}=\frac{13}{2} y+\frac{13}{2}=-\frac{13}{2}$$

Subtract \frac{13}{2} from both sides of the equation.

$$y=0 y=-13$$