
Completing the square.
I need to solve this equation by completing the square:
2x^2 + x  8 = 0
In my textbook the answer is x = 1.77 or x = 2.27
I've tried to do it but can't get the right answer...
2x^2 + x  8 = 0
x^2 + 0.5x  4 = 0
x^2 + 0.5x = 4
x^2 + 0.5x + 0.0625 = 4.0625
(x + 0.0625)^2 = 4.0625
x + 0.0625 = (+/)sqrt4.0625
x =  0.0625 + sqrt4.0625 or x =  00625  sqrt4.0625
x = 1.95... or x = 2.07...
Thanks.

Ok, so we have the equation:
$\displaystyle 2x^2 + x  8 = 0$
Step 1: Move the term without an x to the other side of the equation:
$\displaystyle 2x^2 + x = 8$
Step 2: get the $\displaystyle x^2$ term by itself by dividing by its coefficient:
$\displaystyle x^2 + \frac{1}{2}x = 4$
Step 3: Set aside the coefficient of the xterm and divide it in half:
$\displaystyle \frac{\frac{1}{2}}{2} = \frac{1}{4}$
Step 4: Square the answer:
$\displaystyle \left(\frac{1}{4}\right)^2 = \frac{1}{16}$
Step 5: Add the square to both sides:
$\displaystyle x^2 + \frac{1}{2} + \frac{1}{16} = \frac{65}{16}$
Step 6: Set up the factored form:
$\displaystyle \left(x + \frac{1}{4}\right)^2 = \frac{65}{16}$
Step 7: Take the square root of both sides:
$\displaystyle x + \frac{1}{4} = \pm \frac{\sqrt{65}}{4}$
Step 8: Separate the plus and minus:
$\displaystyle x + \frac{1}{4} = \frac{\sqrt{65}}{4}$
$\displaystyle x + \frac{1}{4} = \frac{\sqrt{65}}{4}$
Step 9: Solve each equation:
$\displaystyle x = \frac{\sqrt{65}1}{4}$
$\displaystyle x = \frac{\sqrt{65}+1}{4}$
Put the fractions in the calculator and you get:
$\displaystyle x \approx 1.7655 \approx 1.77$
$\displaystyle x \approx 2.2655 \approx 2.27$
And there you go.

Thankyou very much.
I think I went wrong when I should have had (x + 1/4)^2 but I had (x + 1/16)^2.