SOLUTION: 2x^2-4x-7=0 solve by completing the square

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Question 147093: 2x^2-4x-7=0 solve by completing the square
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2+x%5E2-4+x-7 Start with the given expression


2%28x%5E2-2x-7%2F2%29 Factor out the leading coefficient 2


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

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




2%28x%5E2-2x%2B1-1-7%2F2%29 Now add and subtract this value inside the parenthesis. Notice how 1-1=0. Since we're adding 0, we're not changing the equation.



2%28%28x-1%29%5E2-1-7%2F2%29 Now factor x%5E2-2x%2B1 to get %28x-1%29%5E2


2%28%28x-1%29%5E2-9%2F2%29 Combine like terms


2%28x-1%29%5E2%2B2%28-9%2F2%29 Distribute


2%28x-1%29%5E2-9 Multiply



So after completing the square, 2x%5E2-4x-7 becomes 2%28x-1%29%5E2-9.


In other words, 2x%5E2-4x-7=2%28x-1%29%5E2-9

So 2x%5E2-4x-7=0 is equivalent to 2%28x-1%29%5E2-9=0


2%28x-1%29%5E2-9=0 Start with the given equation


2%28x-1%29%5E2=9 Add 9 to both sides


%28x-1%29%5E2=9%2F2 Divide both sides by 2


x-1=0%2B-sqrt%289%2F2%29 Take the square root of both sides


x=1%2B-sqrt%289%2F2%29 Add 1 to both sides


x=1%2Bsqrt%289%2F2%29 or x=1-sqrt%289%2F2%29 Break up the plus/minus


x=1%2B3%2Fsqrt%282%29 or x=1-3%2Fsqrt%282%29 Simplify


x=1%2B3sqrt%282%29%2F2 or x=1-3sqrt%282%29%2F2 Rationalize the denominator


So our answers are x=1%2B3sqrt%282%29%2F2 or x=1-3sqrt%282%29%2F2

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
2x%5E2-4x-7=0+

Step 1: Add the constant term to both sides

2x%5E2-4x=7

Step 2: Divide both sides by the lead coefficient

x%5E2-2x=7%2F2

Step 3: Divide the coefficient on the 1st degree term by 2 (%28-2%29%2F2), square the result %28-1%29%5E2=1, then add it to both sides

x%5E2-2x%2B1=7%2F2%2B1

x%5E2-2x%2B1=9%2F2

Step 4: Factor the perfect square on the left

%28x-1%29%5E2=9%2F2

Step 5: Take the square root of both sides

x-1=sqrt%289%2F2%29 or x-1=-sqrt%289%2F2%29

Step 6: Add the constant term on the left to both sides

x=1%2B-sqrt%289%2F2%29

Step 7: Simplify

(Left as an exercise for the student. Remember to rationalize your denominator)