complete the square?

Question

2x^2+10x+11=0

Answer 1

2x^2+10x+11=0

Put the constant on one side of the equation, and the x and x^2 terms on the other:
2x^2 + 10x = -11

Divide both sides by the coefficient of x^2, which is 2:
x^2 + 5x = -11/2

Take half the coefficient of x, square it, and add it to both sides:
x^2 + 5x + 25/4 = -11/2 + 25/4
x^2 + 5x + 25/4 = 3/4

Factor the left side.
(x + 5/2)^2 = 3/4

Notice the number inside the parantheses that you add to x is half the coefficient of x that we got in an earlier step--this will always be the case.

Take the square root of both sides, be sure to include the ± sign for the right side:
√[(x + 5/2)^2] = √(3/4)
x + 5/2 = ± √(3)/2

x = -5/2 + √(3)/2
and
x = -5/2 - √(3)/2

Answer 2

Divide everything by 2
x^2+5x+11/2=0
Subtract the 11/2 to the other side
x^2+5x+ ( )= 11/2+ ( )
x^2+5x+ (5/2)=11/2+(5/2)
(x+5/2)^2=11/2+5/2
(x+5/2)=Square root of 3i

Answer 3

x² + 5x = - 11 / 2
x² + 5x + 25/4 = - 11/2 + 25/4
(x + 5/2)² = - 22/4 + 25/4
(x + 5/2)² = 3/4
(x + 5/2) = ± (1/2).√3
x = - 5/2 ± (1/2)√3
x = (-1/2).(5 ± √3)

Answer 4

2x²+10x+11=0
delta = 10² - 4*2*11
delta = 100 - 88
delta = 12

x = (-10 +/- \/12) : 2*2
x = (-10 + 2\/3) : 4 = -5 + \/3/2
x" = (-10 -2\/3) : 4 = -5 -\/3/2
Solution: {-5 + \/3/2 or -5 -\/3/2}
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Answer 5

2x^2+10x+11=0
2(x^2 + 5x + 5.5) = 0
2[(x+2.5)^2 - (2.5)^2 + 5.5] = 0
2[(x+2.5)^2 - 6.25 + 5.5] = 0
2(x+2.5)^2 - 12.5 + 11 = 0
2(x+2.5)^2 - 1.5 = 0

Answer 6

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