SOLUTION: solve by completing the square 2m^2-m-15=0?

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Question 133088: solve by completing the square 2m^2-m-15=0?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
y=2+x%5E2-1+x-15 Start with the given equation


y%2B15=2+x%5E2-1+x Add 15 to both sides


y%2B15=2%28x%5E2%2B%28-1%2F2%29x%29 Factor out the leading coefficient 2


Take half of the x coefficient -1%2F2 to get -1%2F4 (ie %281%2F2%29%28-1%2F2%29=-1%2F4).

Now square -1%2F4 to get 1%2F16 (ie %28-1%2F4%29%5E2=%28-1%2F4%29%28-1%2F4%29=1%2F16)




y%2B15=2%28x%5E2%2B%28-1%2F2%29x%2B1%2F16-1%2F16%29 Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of 1%2F16 does not change the equation



y%2B15=2%28%28x-1%2F4%29%5E2-1%2F16%29 Now factor x%5E2%2B%28-1%2F2%29x%2B1%2F16 to get %28x-1%2F4%29%5E2


y%2B15=2%28x-1%2F4%29%5E2-2%281%2F16%29 Distribute


y%2B15=2%28x-1%2F4%29%5E2-1%2F8 Multiply


y=2%28x-1%2F4%29%5E2-1%2F8-15 Now add %2B15 to both sides to isolate y


y=2%28x-1%2F4%29%5E2-121%2F8 Combine like terms



2%28x-1%2F4%29%5E2-121%2F8=0 Now to solve for x, let y=0


2%28x-1%2F4%29%5E2=%2B121%2F8 Add 121%2F8 to both sides


%28x-1%2F4%29%5E2=%28121%2F8%29%2F%282%29 Divide both sides by 2


%28x-1%2F4%29%5E2=121%2F16 Reduce


Take the square root of both sides



Take the square root of 121 to get 11. Take the square root of 16 to get 4.


Add 1%2F4 to both sides


Break up the expression

or



Combine the fractions

or


Combine like terms


or



Reduce


or




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Answer:
So our solution is


or