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John D, BS Degree in Engineering.
Category: General
Satisfied Customers: 9666
Experience:  Math, science and 25 years experience in computer programming
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# solve the equation by completing the square 2xsquared-x-6 0

### Resolved Question:

2xsquared-x-6=0
solve the equation by completing the square
Submitted: 9 years ago.
Category: General
Expert:  John D replied 9 years ago.

2xsquared-x-6=0

2x^2 - x - 6 = 0

Solving for x in this quadratic equation, you get two values of x:

x = 2
x = -1.5

Hope this helps.

Expert:  John D replied 9 years ago.

Sorry, did not notice that the problem required to be solved using the "completing the squares" method.

Okay, here is the solution:

2x^2 - x - 6 = 0
x^2 - x/2 - 3 = 0
x^2 - x/2 = 3

Now we need to re write the left side of the equation in the form of x^2 + 2bx + b^2
So the equation becomes:
x^2 + 2(-1/4)x + 1/16 - 1/16 = 3
(x^2 + 2(-1/4)x + 1/16) - 1/16 = 3
(x-1/4)^2 - 1/16 = 3
(x-1/4)^2 = 3 + 1/16
(x-1/4)^2 = 49/16

So there are two solutions:
(x-1/4) = +√(49/16)
(x-1/4) = -√(49/16)

In the first case
(x-1/4) = +√(49/16)
(x-1/4) = 7/4
x = 7/4 + 1/4
x = 8/4
x = 2

In the second case
(x-1/4) = -√(49/16)
(x-1/4) = -7/4
x = -7/4 + 1/4
x = -6/4
x = -1.5