Solve y=y/2y

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

Solve for y

$$y=2$$

$$y=0$$

Steps Using the Quadratic Formula

Express \frac{y}{2}y as a single fraction.

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

Multiply y and y to get y^{2}.

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

Subtract \frac{y^{2}}{2} from both sides.

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

Multiply both sides of the equation by 2.

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

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

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

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

$$y=\frac{-2±\sqrt{2^{2}}}{2\left(-1\right)}$$

Take the square root of 2^{2}.

$$y=\frac{-2±2}{2\left(-1\right)}$$

Multiply 2 times -1.

$$y=\frac{-2±2}{-2}$$

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

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

Divide 0 by -2.

$$y=0$$

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

$$y=-\frac{4}{-2}$$

Divide -4 by -2.

$$y=2$$

The equation is now solved.

$$y=0 y=2$$

Steps for Completing the Square

Express \frac{y}{2}y as a single fraction.

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

Multiply y and y to get y^{2}.

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

Subtract \frac{y^{2}}{2} from both sides.

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

Multiply both sides of the equation by 2.

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

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

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

Divide both sides by -1.

$$\frac{-y^{2}+2y}{-1}=\frac{0}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$y^{2}+\frac{2}{-1}y=\frac{0}{-1}$$

Divide 2 by -1.

$$y^{2}-2y=\frac{0}{-1}$$

Divide 0 by -1.

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

Divide -2, the coefficient of the x term, by 2 to get -1. Then add the square of -1 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$y^{2}-2y+1=1$$

Factor y^{2}-2y+1. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(y-1\right)^{2}=1$$

Take the square root of both sides of the equation.

$$\sqrt{\left(y-1\right)^{2}}=\sqrt{1}$$

Simplify.

$$y-1=1 y-1=-1$$

Add 1 to both sides of the equation.

$$y=2 y=0$$