Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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.

Answer 6

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

Answer 7

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