SOLUTION: Solve the following quadratic equation by completing the square. 2x^2+10x+11=0

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Solve the following quadratic equation by completing the square. 2x^2+10x+11=0      Log On


   

Question 124292: Solve the following quadratic equation by completing the square.
2x^2+10x+11=0
Found 3 solutions by jim_thompson5910, edjones, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
y=2+x%5E2%2B10+x%2B11 Start with the given equation


y-11=2+x%5E2%2B10+x Subtract 11 from both sides


y-11=2%28x%5E2%2B5x%29 Factor out the leading coefficient 2


Take half of the x coefficient 5 to get 5%2F2 (ie %281%2F2%29%285%29=5%2F2).

Now square 5%2F2 to get 25%2F4 (ie %285%2F2%29%5E2=%285%2F2%29%285%2F2%29=25%2F4)




y-11=2%28x%5E2%2B5x%2B25%2F4-25%2F4%29 Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of 25%2F4 does not change the equation



y-11=2%28%28x%2B5%2F2%29%5E2-25%2F4%29 Now factor x%5E2%2B5x%2B25%2F4 to get %28x%2B5%2F2%29%5E2


y-11=2%28x%2B5%2F2%29%5E2-2%2825%2F4%29 Distribute


y-11=2%28x%2B5%2F2%29%5E2-25%2F2 Multiply


y=2%28x%2B5%2F2%29%5E2-25%2F2%2B11 Now add 11 to both sides to isolate y


y=2%28x%2B5%2F2%29%5E2-3%2F2 Combine like terms



2%28x%2B5%2F2%29%5E2-3%2F2=0 Now to solve for x, let y=0


2%28x%2B5%2F2%29%5E2=%2B3%2F2 Add 3%2F2 to both sides


%28x%2B5%2F2%29%5E2=%283%2F2%29%2F%282%29 Divide both sides by 2


%28x%2B5%2F2%29%5E2=3%2F4 Reduce


Take the square root of both sides


Simplify sqrt%283%2F4%29 to get sqrt%283%29%2F2


Subtract 5%2F2 from both sides


Combine the fractions



So our solutions are

or



Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
2x^2+10x+11=0
x^2+5x+5.5=0 divide each side by 5.5
x^2+5x+6.25=-5.5+6.25 complete the square by dividing 5 by 2 and suaring the result.
(x+2.5)^2=.75
x+2.5=+-sqrt(.75)
x=-2.5+.866= -1.634
x=-2.5-.866= -3.366
.
Ed

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the following quadratic equation by completing the square.
2x^2+10x+11=0
--------------------------
Divide thru by 2 to get:
x^2+5x+(11/2)=0
Complete the square on the x-terms.
x^2+5x+(5/2)^2 = (-11/2)+(5/2)^2
(x+(5/2))^2 = (-22/4) + (25/4)
(x+(5/2))^2 = 1
x+(5/2) = 1 or x+(5/2)= -1
x = -3/2 or x = -7/2
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Cheers,
Stan H.