Converting standard form into vertex form?

Question

I converted $5x^2 - 5x = 30$ into it's vertex form, and I just want to confirm my answer.

Here is what I did:

$5x^2 - 5x = 30$

$5x^2 - 5x - 30 = 0$

$5(x^2 - x - 6) = 0$

$5(x^2 - x) = 6$

$5(x^2 - x - (\frac{1}{2})^2) = 6 - (\frac{1}{2})^2$

$5(x^2 - x + \frac{1}{4}) = 6 + \frac{1}{4}$

$5(x^2 - x + \frac{1}{4}) = 6.25$

$5(x - \frac{1}{2})^2 - 6.25 = 0$

Is it right?

Answer 1

Mistake from

$$5(x^2-x-6)=0$$

to $$\color{green}{5}(x^2-x)=6$$

Also even though you wrote $-\left(\frac12\right)^2$, you actually meant $+\left(\frac12\right)^2$.

Quickest way to fix this is to get rid of the $5$ that I colored in green.

$$(x-\frac12)^2-6.25=0$$ is the vertex form.