Solve by completing the square.?

Question

2x^2 - 8x - 11 = 0

Answer 1

Add 11 to both sides. Divide everything by 2

You now have:

x^2-4x = 11/2

Divide the middle term by 2 and square that result. Add to both sides of the equaltion to get:

x^2 - 2x + 4 = 11/2 + 4

(x-2)^2 = 19/2

x-2 = +- sqrt (19/2)

x = 2 +- sqrt (19/2)

+- means plus/minus

Answer 2

Completing the square

2x² - 8x - 11 = 0
+11 +11

subtract + 11from both sides

2x² - 8x + 16 = 11

2x²/2 - 8x/2 = 11/2

dividing through the equation by 2

x² - 4x = 11/2

x² -4x + 4 = 11/2 + 4

divide - 4x in half equals 2. 2² = 4. add 4 to both sides

x² - 4x + 4 = 11/2 + 8/2

the common denominator on the right side of the equation is 2

x² - 4x + 4 = 19/2

(x - 2)(x - 2) = ± √19/2

or

(x - 2)² = ± √19/2

(x - 2)² = ± √19/2

x = 2 ± √19/2

The answer is x = 2 ± √19/2

Answer 3

2x^2 - 8x - 11 = 0
(2x^2 - 8x - 11)/2 = 0/2. Here we divide by sides of eq by 2.
x^2 - 4x - 11/2 = 0
(x - 2)^2 - 11/2 - 4 =0 because we have to subtract the 4 that the (-2)^2 in the (x - 2)^2 generates.
Now we get
(x - 2)^2 - 19/2 = 0
(x - 2)^2 = 19/2
(x - 2) =+/-sqrt(19/2)
x = 2 +/- sqrt(19/2). Here we have 2 real roots.
So,
x = 2 + sqrt (19/2), 2 - sqrt(19/2)

Answer 4

2 x^2 - 8x - 11 = 0
2 x^2 -8x = 11
x^2 - 4x = 11/2
x^2 - 4x + 4 = 11/2 + 4
(x - 2)^2 = 19/2
x - 2 = +- sqrt(19/2)
x = 2 +- sqrt (19/2)

Answer 5

2x^2 - 8x - 11 = 0
2x^2 - 8x = 11
x^2 - 4x = (11/2)
x^2 - 4x + 4 = (19/2)
(x - 2)^2 = (19/2)
x - 2 = ±sqrt(19/2)
x - 2 = sqrt(38)/2
x = 2 ± (sqrt(38)/2)
x = (1/2)(4 ± sqrt(38))

x = (1/2)(4 + sqrt(38)) or (1/2)(4 - sqrt(38))

Answer 6

2x^2 - 8x - 11 = 0
2 [x^2 - 4x + 4] - 8 - 11 = 0
2[(x - 2) ^2] - 19 = 0
2(x - 2)^2 = 19
(x-2)^2 = 19/2
(x-2) = (19/2)^0.5 or (x-2) = -(19/2)^0.5
x = 2 + (19/2)^0.5 or x = 2 - (19/2)^0.5

Good luck!
=)

Answer 7

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