SOLUTION: Solve each of the following quadratic equations by completing the square. 2x2 + 10x + 11 = 0

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Solve each of the following quadratic equations by completing the square. 2x2 + 10x + 11 = 0       Log On


   

Question 115423: Solve each of the following quadratic equations by completing the square.
2x2 + 10x + 11 = 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 5%2F2
Now square 5%2F2 to get 25%2F4



2%28x%5E2%2B5x%2B25%2F4%29=-11%2B%2825%2F4%29%282%29 Add this result 25%2F4 to the expression x%5E2%2B5x inside the parenthesis. Now the expression x%5E2%2B5x%2B25%2F4 is a perfect square trinomial. Now add the result %2825%2F4%29%282%29 (remember we factored out a 2) to the right side.



2%28x%2B5%2F2%29%5E2=-11%2B%2825%2F4%29%282%29 Factor x%5E2%2B5x%2B25%2F4 into %28x%2B5%2F2%29%5E2


2%28x%2B5%2F2%29%5E2=-11%2B25%2F2 Multiply 25%2F4 and 2 to get 25%2F2



2%28x%2B5%2F2%29%5E2=3%2F2 Combine like terms on the right side

%28x%2B5%2F2%29%5E2=3%2F4 Divide both sides by 2


x%2B5%2F2=0%2B-sqrt%283%2F4%29 Take the square root of both sides


x%2B5%2F2=0%2B-sqrt%283%29%2Fsqrt%284%29 Break up the square root


x%2B5%2F2=0%2B-sqrt%283%29%2F2 Take the square root of 4 to get 2


x=-5%2F2%2B-sqrt%283%29%2F2 Subtract 5%2F2 from both sides to isolate x.


x=%28-5%2B-sqrt%283%29%29%2F2 Combine the fractions



So our answer is
x=%28-5%2Bsqrt%283%29%29%2F2 or x=%28-5-sqrt%283%29%29%2F2