Solve y^2=18y

$$y ^ { 2 } = 18 y$$

Solve for y

$$y=18$$

$$y=0$$

Steps Using Factoring

Subtract 18y from both sides.

$$y^{2}-18y=0$$

Factor out y.

$$y\left(y-18\right)=0$$

To find equation solutions, solve y=0 and y-18=0.

$$y=0 y=18$$

Steps Using the Quadratic Formula

Subtract 18y from both sides.

$$y^{2}-18y=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -18 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{-\left(-18\right)±\sqrt{\left(-18\right)^{2}}}{2}$$

Take the square root of \left(-18\right)^{2}.

$$y=\frac{-\left(-18\right)±18}{2}$$

The opposite of -18 is 18.

$$y=\frac{18±18}{2}$$

Now solve the equation y=\frac{18±18}{2} when ± is plus. Add 18 to 18.

$$y=\frac{36}{2}$$

Divide 36 by 2.

$$y=18$$

Now solve the equation y=\frac{18±18}{2} when ± is minus. Subtract 18 from 18.

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

Divide 0 by 2.

$$y=0$$

The equation is now solved.

$$y=18 y=0$$

Steps for Completing the Square

Subtract 18y from both sides.

$$y^{2}-18y=0$$

Divide -18, the coefficient of the x term, by 2 to get -9. Then add the square of -9 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$y^{2}-18y+\left(-9\right)^{2}=\left(-9\right)^{2}$$

Square -9.

$$y^{2}-18y+81=81$$

Factor y^{2}-18y+81. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(y-9\right)^{2}=81$$

Take the square root of both sides of the equation.

$$\sqrt{\left(y-9\right)^{2}}=\sqrt{81}$$

Simplify.

$$y-9=9 y-9=-9$$

Add 9 to both sides of the equation.

$$y=18 y=0$$