Solving with the Quadratic Formula

[bcroes]

I'm having difficulty on a problem that deals with the Quadratic Formula.

-(-4) +_ sqrt (-4)^2-4(2)(1)
2(2)

4 +_ sqrt 8
4

4 +_ 2 sqrt 2
4

This is where I get stuck, the below is what I come up with...
4 +_ 2 sqrt 2
4

and this is what the book shows...
2 +_ sqrt 2
2

Please help me find the step I'm missing. Thanks!

 

[soroban]

Hello, bcroes!

I'm having difficulty on a problem that deals with the Quadratic Formula.

\(\displaystyle x \;=\;\frac{]-(-4) \pm \sqrt{(-4)^2-4(2)(1)}}{2(2)} \;=\;\frac{4 \pm \sqrt{8}}{4} \;=\;\frac{4 \pm 2\sqrt{2}}{4}\)

\(\displaystyle \text{But the book shows: }\;x \;=\;\frac{2 \pm \sqrt{2}}{2}\)

Please help me find the step I'm missing. Thanks!

\(\displaystyle \text{Your work is correct: }\;x \;=\;\frac{4 \pm 2\sqrt{2}}{4}\)

\(\displaystyle Factor\text{ the numerator: }\;x \;=\;\frac{2(2 \pm\sqrt{2})}{4}\)

\(\displaystyle \text{Then reduce: }\;x \;=\;\frac{\rlap{/}2(2\pm\sqrt{2})}{\rlap{/}4_2} \;=\;\frac{2\pm\sqrt{2}}{2}\)