SOLUTION: Complete the square for 2x2 + 5x – 1 = 0

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Question 161351: Complete the square for 2x2 + 5x – 1 = 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

2x%5E2%2B5x-1 Start with the given expression.


2%28x%5E2%2B%285%2F2%29x-1%2F2%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 5%2F2 to get 5%2F4. In other words, %281%2F2%29%285%2F2%29=5%2F4.


Now square 5%2F4 to get 25%2F16. In other words, %285%2F4%29%5E2=%285%2F4%29%285%2F4%29=25%2F16


2%28x%5E2%2B%285%2F2%29x%2Bhighlight%2825%2F16-25%2F16%29-1%2F2%29 Now add and subtract 25%2F16 inside the parenthesis. Make sure to place this after the "x" term. Notice how 25%2F16-25%2F16=0. So the expression is not changed.


2%28%28x%5E2%2B%285%2F2%29x%2B25%2F16%29-25%2F16-1%2F2%29 Group the first three terms.


2%28%28x%2B5%2F4%29%5E2-25%2F16-1%2F2%29 Factor x%5E2%2B%285%2F2%29x%2B25%2F16 to get %28x%2B5%2F4%29%5E2.


2%28%28x%2B5%2F4%29%5E2-33%2F16%29 Combine like terms.


2%28x%2B5%2F4%29%5E2%2B2%28-33%2F16%29 Distribute.


2%28x%2B5%2F4%29%5E2-33%2F8 Multiply.


So after completing the square, 2x%5E2%2B5x-1 transforms to 2%28x%2B5%2F4%29%5E2-33%2F8. So 2x%5E2%2B5x-1=2%28x%2B5%2F4%29%5E2-33%2F8.


So 2x%5E2%2B5x-1=0 is equivalent to 2%28x%2B5%2F4%29%5E2-33%2F8=0.