Using the Quadratic Formula to Find Solutions (not understanding factorization)

[Dirty.Rotten.Imbecile]

Hi, I was able to work this out up to where I have marked with a red A. I am not sure how the author could put multiplication brackets around the expression as shown where I marked it with a red B.

The 2 that was previously rooted out of 88 moves to the left of the +/-. Why is that? I don’t follow how this was done.

Can anyone explain?

 

[Dirty.Rotten.Imbecile]

I guess that’s what doesn’t make sense to me. In your first example, 2 is factored out of each term but 2 is not factored out of the square root of 22 in my example.

 

[tkhunny]

I guess that’s what doesn’t make sense to me. In your first example, 2 is factored out of each term but 2 is not factored out of the square root of 22 in my example.

1) Get a different screen name. We prefer a learning and trying attitude.

2) There are general ideas to simplify. When moving things out of a square root, we would do that normally ONLY if there is a perfect square on the inside.

\(\displaystyle \sqrt{44} = \sqrt{4\cdot 11} = \sqrt{4}\cdot\sqrt{11} = 2\cdot\sqrt{11}\)

\(\displaystyle \sqrt{22} = \sqrt{2\cdot 11}\) -- No perfect square in there.

 

[Steven G]

View attachment 9605
Hi, I was able to work this out up to where I have marked with a red A. I am not sure how the author could put multiplication brackets around the expression as shown where I marked it with a red B.

The 2 that was previously rooted out of 88 moves to the left of the +/-. Why is that? I don’t follow how this was done.

Can anyone explain?

Here is a hint. Suppose x = yz (y and z are NOT both negative) and sqrt(y)=w. Then sqrt(x) = sqrt(yz) = sqrt(y)*sqrt(z) = w*sqrt(z). Also, sqrt(4)=2.

 

[JeffM]

View attachment 9605
The 2 that was previously rooted out of 88 moves to the left of the +/-. Why is that? I don’t follow how this was done.

The two that was extracted from the square root of 88 was not moved anywhere. The numerator as a whole was factored by two and then that two was cancelled against the two in the denominator. When you don't understand something, try doing it in baby steps.

\(\displaystyle x = \dfrac{4 \pm \sqrt{88}}{4} = \dfrac{4 \pm \sqrt{4 * 11}}{4} = \dfrac{4 \pm \sqrt{4} * \sqrt{11}}{4} =\)

\(\displaystyle \dfrac{4 \pm 2 * \sqrt{11}}{4} = \dfrac{2(2 \pm \sqrt{11})}{2 * 2} = \dfrac{2 \pm \sqrt{11}}{2}.\)

 

[Dirty.Rotten.Imbecile]

I appreciate the help everyone. I think I was overloaded on Quadratic Equations yesterday. It all makes sense now.

Seeing it broken down into baby steps helped a lot.