SOLUTION: Could someone please help me with this equation? Solve this quadratic equation by completing the square. {{{2x^2+10x+11=0}}}

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Question 100449: Could someone please help me with this equation? Solve this quadratic equation by completing the square.
2x%5E2%2B10x%2B11=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

2x%5E2%2B10x%2B11=0 Start with the given equation


2x%5E2%2B10x=-11 Subtract 11 from both sides
2%28x%5E2%2B5x%29=-11 Factor out the leading coefficient 2. This step is important since we want the x%5E2 coefficient to be equal to 1.



Take half of the x coefficient 5 to get 2.5 (ie 5%2F2=2.5)
Now square 2.5 to get 6.25 (ie %282.5%29%5E2=6.25)



2%28x%5E2%2B5x%2B6.25%29=-11%2B6.25%282%29 Add this result (6.25) to the expression x%5E2%2B5x inside the parenthesis. Now the expression x%5E2%2B5x%2B6.25 is a perfect square trinomial. Now add the result (6.25)(2) (remember we factored out a 2) to the right side.



2%28x%2B2.5%29%5E2=-11%2B6.25%282%29 Factor x%5E2%2B5x%2B6.25 into %28x%2B2.5%29%5E2


2%28x%2B2.5%29%5E2=-11%2B12.5 Multiply 6.25 and 2 to get 12.5



2%28x%2B2.5%29%5E2=1.5 Combine like terms on the right side

%28x%2B2.5%29%5E2=0.75 Divide both sides by 2


x%2B2.5=0%2B-sqrt%280.75%29 Take the square root of both sides

x=-2.5%2B-sqrt%280.75%29 Subtract 2.5 from both sides to isolate x.

So the expression breaks down to
x=-2.5%2Bsqrt%280.75%29 or x=-2.5-sqrt%280.75%29


So our answer is approximately
x=-1.63397459621556 or x=-3.36602540378444

Here is visual proof

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+2x%5E2%2B10x%2B11%29+ graph of y=2x%5E2%2B10x%2B11


When we use the root finder feature on a calculator, we would find that the x-intercepts are x=-1.63397459621556 and x=-3.36602540378444, so this verifies our answer.