SOLUTION: I am confused if anyone could help It would be appreciated.I don't understand how to finish the problem Solve by completing the square. 2x^2 - 3x + 1 = 0 This is what I have so

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I am confused if anyone could help It would be appreciated.I don't understand how to finish the problem Solve by completing the square. 2x^2 - 3x + 1 = 0 This is what I have so      Log On


   

Question 203132: I am confused if anyone could help It would be appreciated.I don't understand how to finish the problem
Solve by completing the square.
2x^2 - 3x + 1 = 0
This is what I have so far
a=2 b=3 c=1
2x^2 - 3x + 1 = 0
x^2 - 3/2 x 1/2
x^2 - 3/2x + 3/4
now I am lost
Found 2 solutions by vleith, ptaylor:
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!

Here is solver you can use for this --> http://www.algebra.com/algebra/homework/quadratic/complete-square.solver
Solved by pluggable solver: COMPLETING THE SQUARE solver for quadratics
Read this lesson on completing the square by prince_abubu, if you do not know how to complete the square.
Let's convert 2x%5E2%2B-3x%2B1=0 to standard form by dividing both sides by 2:
We have: 1x%5E2%2B-1.5x%2B0.5=0. What we want to do now is to change this equation to a complete square %28x%2Bsomenumber%29%5E2+%2B+othernumber. How can we find out values of somenumber and othernumber that would make it work?
Look at %28x%2Bsomenumber%29%5E2: %28x%2Bsomenumber%29%5E2+=+x%5E2%2B2%2Asomenumber%2Ax+%2B+somenumber%5E2. Since the coefficient in our equation 1x%5E2%2Bhighlight_red%28+-1.5%29+%2A+x%2B0.5=0 that goes in front of x is -1.5, we know that -1.5=2*somenumber, or somenumber+=+-1.5%2F2. So, we know that our equation can be rewritten as %28x%2B-1.5%2F2%29%5E2+%2B+othernumber, and we do not yet know the other number.
We are almost there. Finding the other number is simply a matter of not making too many mistakes. We need to find 'other number' such that %28x%2B-1.5%2F2%29%5E2+%2B+othernumber is equivalent to our original equation 1x%5E2%2B-1.5x%2Bhighlight_green%28+0.5+%29=0.


The highlighted red part must be equal to 0.5 (highlighted green part).

-1.5%5E2%2F4+%2B+othernumber+=+0.5, or othernumber+=+0.5--1.5%5E2%2F4+=+-0.0625.
So, the equation converts to %28x%2B-1.5%2F2%29%5E2+%2B+-0.0625+=+0, or %28x%2B-1.5%2F2%29%5E2+=+0.0625.

Our equation converted to a square %28x%2B-1.5%2F2%29%5E2, equated to a number (0.0625).

Since the right part 0.0625 is greater than zero, there are two solutions:


, or

system%28+%28x%2B-1.5%2F2%29+=+0.25%2C+%28x%2B-1.5%2F2%29+=+-0.25+%29
system%28+x%2B-1.5%2F2+=+0.25%2C+x%2B-1.5%2F2+=+-0.25+%29
system%28+x+=+0.25--1.5%2F2%2C+x+=+-0.25--1.5%2F2+%29

system%28+x+=+1%2C+x+=+0.5+%29
Answer: x=1, 0.5.

Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!

OK, YOU AARE ON THE RIGHT TRACK!!You came up at one point with x^2-3/2x+1/2=0. So lets go from there:
x^2-3/2x+1/2=0 subtract 1/2 from each side
x^2-3/2x=-1/2
Now what do we have to add to the left side (and the right side as well) to make the left side a perfect square in the form of (x-?)^2. Let's expand using foil:
(x-?)^2=x^2-?x-?x+?^2. Now we know that the -?x and -?x must add up to (-3/2)x, so -2?x=(-3/2)x. Cancel the x's and we have -2?=-3/2 then ?=3/4 and ?^2=9/16. So we have to add 9/16 to the left side (and also the right side) to make the left side a perfect square. This gives us:
x^2-3/2x+9/16=-1/2+9/16=1/16 or
(x-3/4)^2=1/16 take square root of both sides
x-3/4=+or-1/4
x=+or-1/4+3/4
x=1 and
x=1/2

Hope this helps---ptaylor