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

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)   (Show Source): You can put this solution on YOUR website!
Start with the given equation

Subtract from both sides

Factor out the leading coefficient

Take half of the x coefficient to get (ie ).

Now square to get (ie )

Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of does not change the equation

Now factor to get

Distribute

Multiply

Now add to both sides to isolate y

Combine like terms

Now to solve for x, let

Add to both sides

Divide both sides by

Reduce

Take the square root of both sides

Simplify to get

Subtract from both sides

Combine the fractions

So our solutions are

or

Answer by edjones(8007)   (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)   (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
=============
Cheers,
Stan H.
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