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# solve the equation by completing the square 2xsquared-x-6 0

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2xsquared-x-6=0 solve the equation by completing...
2xsquared-x-6=0
solve the equation by completing the square
Submitted: 10 years ago.Category: General
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Answered in 7 minutes by:
9/15/2007
Expert: John D, BS Degree in Engineering. replied 10 years ago
John D, BS Degree in Engineering.
Category: General
Satisfied Customers: 9,666
Experience: Math, science and 25 years experience in computer programming
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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.

John D, BS Degree in Engineering.
Category: General
Satisfied Customers: 9,666
Experience: Math, science and 25 years experience in computer programming
Verified
John D and 87 other General Specialists are ready to help you
Expert: John D, BS Degree in Engineering. replied 10 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

John D, BS Degree in Engineering.
Category: General
Satisfied Customers: 9,666
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Experience: Math, science and 25 years experience in computer programming

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