Solve by completing the square: y = x²+7x+12

Question

espex · Answer

You need to first put it in the form of $-12=x^2+7x$

espex · Answer

Then you will be able to use the steps necessary to complete the square.

anonymous · Answer

but I would have to divide 7 by 2 and square it. how would I do that?

kinggeorge · Answer

Well, instead of writing 7/2 as 3.5, leave it as a fraction. What's $$\left(\frac72\right)\left(\frac72\right)?$$

espex · Answer

Squaring 3.5 seems like a trivial task, but as @KingGeorge pointed out, you do not have to reduce to a decimal, you can leave everything as a fraction while you work the equation.

dumbcow · Answer

$$x^{2} +7x + (\frac{7}{2})^{2} = -12 + (\frac{7}{2})^{2}$$
$$x^{2} +7x +\frac{49}{4} = -12 + \frac{49}{4}$$

dumbcow · Answer

$$\rightarrow (x+\frac{7}{2})^{2} = \frac{-48+49}{4}$$
$$(x+\frac{7}{2})^{2} = \frac{1}{4}$$