Why does 2x^2-8x-3=0 get solved this way by completing the square?

Question

By completing the square, I eventually arrive at
(x-2)^2=11/2
then
x-2=+/-sqrt(11/2)
then:
x = 2+/-sqrt(11/2)

But my textbook and answers on yahoo somehow turn that into :
x=2+/-srt(22)/2
I don't understand what I am doing wrong.

First poster, thanks for that, but I don't understand how sqrt(11/2) = (sqrt22)/2

Can you explain please?

Answer 1

Your answer is correct but the denominator needed to be rationalized.

2x² - 8x - 3 = 0

divide the equation by 2

2x² / 2 - 8x / 2 - 3/2 = 0 / 2

x² - 4x - 3/2 = 0

x² - 4x - 3/2 + 3/2 = 0 + 3/2

x² - 4x = 3/2

x² - 4x +_____= 3/2 +_____

x² - 4x + 4 = 3/2 + 4

(x - 2)(x - 2) = 3/2 + 8/2

(x - 2)² = 11/2

(√x - 2)² = ± √11 / 2

x - 2 = ± √11 / √2

x - 2 + 2 = 2 ± √11 / √2

x = 2 ± √11 / √2

Rationalizing the denominator

x = 2 ± √11 √2 / √2 √2

x = 2 ± √22 / √4

x = 2 ± √22 / 2

- - - - - - - -s-

Answer 2

This is a case of rationlizing the denominator. √(11/2) = √11 / √2 = √(11 * 2) / √(2 * 2) = √22 / √4 = √22 / 2 . You are correct, but your answer was not in what is considered simplest form, with no radical in the denominator.

Answer 3

sqrt(11/2) = sqrt(11)/sqrt(2)

multiply by sqrt(2)/sqrt(2) to remove the radical from the denominator, and you have:

sqrt(11) * sqrt(2) / (sqrt(2) * sqrt(2))

And that simplifies to:

sqrt(11 * 2) / sqrt(2)^2

sqrt(22)/2

Answer 4

sqrt(11/2) = (sqrt22)/2

Theres nothing wrong with your answer