# Thread: Solve by completing the square

1. ## Solve by completing the square

Must solve by completing the square

(y^2)+3=(y/2)

thx, I really can't get this one and I'm also pretty sure there are no solutions so I don't really understand what my teacher wants

2. Originally Posted by jorygoldsmith
Must solve by completing the square

(y^2)+3=(y/2)

thx, I really can't get this one and I'm also pretty sure there are no solutions so I don't really understand what my teacher wants
$\displaystyle y^2 - \frac{y}{2} = -3$

$\displaystyle y^2 - \frac{y}{2} + \frac{1}{16} = -3 + \frac{1}{16}
$

$\displaystyle \left(y - \frac{1}{4}\right)^2 = -\frac{47}{16}$

now you can say for sure that $y$ has no real solutions.

3. First, rearrange.

$y^2-\frac{1}{2}y=-3$

Then, $\left(\frac{b}{2}\right)^2$

Add to both sides and simplify.