I need some assistance with a specific problem where the equation given is
$-3x^2-3x+9=0$
I have divided everything by $-3$ to get
$x^2+x-3=0$
Then I move the $3$ to the other side
$x^2+x=3$
Then I complete the square, in this case, what I need to add to complete it is $.25$
$x^2+x+.25=3.25$
Then I factor
$(x+.5)^2=3.25$
Then I take the square root
$x+.5=\sqrt{3.25}$
$\sqrt{3.25}$ is one of the answers to the problem are $x = -1/2,+/-\sqrt{13}/2$
How can the -1/2 part be found?
Any help is appreciated, thank you
Best Answer
When you take the square root, you should account for both possibilities:
$$x+.5 = \pm \sqrt{3.25}.$$
Then subtract $.5$ from both sides:
$$x = -.5 \pm \sqrt{3.25}.$$
If you convert your decimals into fractions, you have
$$x = -\frac{1}{2} \pm \sqrt{\frac{13}{4}} = -\frac{1}{2} \pm \frac{\sqrt{13}}{2}.$$