SOLUTION: Solving Quadraticc Equations by Completing the Square 2x^2 - x + 6 = 0 Thank you for your time and help.

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Question 357118: Solving Quadraticc Equations by Completing the Square
2x^2 - x + 6 = 0
Thank you for your time and help.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2x%5E2-x%2B6 Start with the given expression.


2%28x%5E2-%281%2F2%29x%2B3%29 Factor out the x%5E2 coefficient 2. This step is very important: the x%5E2 coefficient must be equal to 1.


Take half of the x coefficient -1%2F2 to get -1%2F4. In other words, %281%2F2%29%28-1%2F2%29=-1%2F4.


Now square -1%2F4 to get 1%2F16. In other words, %28-1%2F4%29%5E2=%28-1%2F4%29%28-1%2F4%29=1%2F16


2%28x%5E2-%281%2F2%29x%2Bhighlight%281%2F16-1%2F16%29%2B3%29 Now add and subtract 1%2F16 inside the parenthesis. Make sure to place this after the "x" term. Notice how 1%2F16-1%2F16=0. So the expression is not changed.


2%28%28x%5E2-%281%2F2%29x%2B1%2F16%29-1%2F16%2B3%29 Group the first three terms.


2%28%28x-1%2F4%29%5E2-1%2F16%2B3%29 Factor x%5E2-%281%2F2%29x%2B1%2F16 to get %28x-1%2F4%29%5E2.


2%28%28x-1%2F4%29%5E2%2B47%2F16%29 Combine like terms.


2%28x-1%2F4%29%5E2%2B2%2847%2F16%29 Distribute.


2%28x-1%2F4%29%5E2%2B47%2F8 Multiply.


So after completing the square, 2x%5E2-x%2B6 transforms to 2%28x-1%2F4%29%5E2%2B47%2F8. So 2x%5E2-x%2B6=2%28x-1%2F4%29%5E2%2B47%2F8.


So 2x%5E2-x%2B6=0 is equivalent to 2%28x-1%2F4%29%5E2%2B47%2F8=0.


Now let's solve 2%28x-1%2F4%29%5E2%2B47%2F8=0


2%28x-1%2F4%29%5E2%2B47%2F8=0 Start with the given equation.


2%28x-1%2F4%29%5E2=0-47%2F8Subtract 47%2F8 from both sides.


2%28x-1%2F4%29%5E2=-47%2F8 Combine like terms.


%28x-1%2F4%29%5E2=%28-47%2F8%29%2F%282%29 Divide both sides by 2.


%28x-1%2F4%29%5E2=-47%2F16 Reduce.


x-1%2F4=%22%22%2B-sqrt%28-47%2F16%29 Take the square root of both sides.


x-1%2F4=sqrt%28-47%2F16%29 or x-1%2F4=-sqrt%28-47%2F16%29 Break up the "plus/minus" to form two equations.


x-1%2F4=i%2A%28sqrt%2847%29%29%2F4%29 or x-1%2F4=-i%2A%28sqrt%2847%29%29%2F4%29 Simplify the square root.


x=1%2F4%2Bi%2A%28sqrt%2847%29%29%2F4%29 or x=1%2F4-i%2A%28sqrt%2847%29%29%2F4%29 Add 1%2F4 to both sides.


x=%281%2Bi%2Asqrt%2847%29%29%2F4 or x=%281-i%2Asqrt%2847%29%29%2F4 Combine the fractions.


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Answer:


So the solutions are x=%281%2Bi%2Asqrt%2847%29%29%2F4 or x=%281-i%2Asqrt%2847%29%29%2F4 where i=sqrt%28-1%29.


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim