0.5k(11-k)+(6-(k+1))=0.5(k+1)(11-k+1)

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Solution for 0.5k(11-k)+(6-(k+1))=0.5(k+1)(11-k+1) equation: 


Simplifying
0.5k(11 + -1k) + (6 + -1(k + 1)) = 0.5(k + 1)(11 + -1k + 1)
(11 * 0.5k + -1k * 0.5k) + (6 + -1(k + 1)) = 0.5(k + 1)(11 + -1k + 1)
(5.5k + -0.5k2) + (6 + -1(k + 1)) = 0.5(k + 1)(11 + -1k + 1)

Reorder the terms:
5.5k + -0.5k2 + (6 + -1(1 + k)) = 0.5(k + 1)(11 + -1k + 1)
5.5k + -0.5k2 + (6 + (1 * -1 + k * -1)) = 0.5(k + 1)(11 + -1k + 1)
5.5k + -0.5k2 + (6 + (-1 + -1k)) = 0.5(k + 1)(11 + -1k + 1)

Combine like terms: 6 + -1 = 5
5.5k + -0.5k2 + (5 + -1k) = 0.5(k + 1)(11 + -1k + 1)

Remove parenthesis around (5 + -1k)
5.5k + -0.5k2 + 5 + -1k = 0.5(k + 1)(11 + -1k + 1)

Reorder the terms:
5 + 5.5k + -1k + -0.5k2 = 0.5(k + 1)(11 + -1k + 1)

Combine like terms: 5.5k + -1k = 4.5k
5 + 4.5k + -0.5k2 = 0.5(k + 1)(11 + -1k + 1)

Reorder the terms:
5 + 4.5k + -0.5k2 = 0.5(1 + k)(11 + -1k + 1)

Reorder the terms:
5 + 4.5k + -0.5k2 = 0.5(1 + k)(11 + 1 + -1k)

Combine like terms: 11 + 1 = 12
5 + 4.5k + -0.5k2 = 0.5(1 + k)(12 + -1k)

Multiply (1 + k) * (12 + -1k)
5 + 4.5k + -0.5k2 = 0.5(1(12 + -1k) + k(12 + -1k))
5 + 4.5k + -0.5k2 = 0.5((12 * 1 + -1k * 1) + k(12 + -1k))
5 + 4.5k + -0.5k2 = 0.5((12 + -1k) + k(12 + -1k))
5 + 4.5k + -0.5k2 = 0.5(12 + -1k + (12 * k + -1k * k))
5 + 4.5k + -0.5k2 = 0.5(12 + -1k + (12k + -1k2))

Combine like terms: -1k + 12k = 11k
5 + 4.5k + -0.5k2 = 0.5(12 + 11k + -1k2)
5 + 4.5k + -0.5k2 = (12 * 0.5 + 11k * 0.5 + -1k2 * 0.5)
5 + 4.5k + -0.5k2 = (6 + 5.5k + -0.5k2)

Add '0.5k2' to each side of the equation.
5 + 4.5k + -0.5k2 + 0.5k2 = 6 + 5.5k + -0.5k2 + 0.5k2

Combine like terms: -0.5k2 + 0.5k2 = 0.0
5 + 4.5k + 0.0 = 6 + 5.5k + -0.5k2 + 0.5k2
5 + 4.5k = 6 + 5.5k + -0.5k2 + 0.5k2

Combine like terms: -0.5k2 + 0.5k2 = 0.0
5 + 4.5k = 6 + 5.5k + 0.0
5 + 4.5k = 6 + 5.5k

Solving
5 + 4.5k = 6 + 5.5k

Solving for variable 'k'.

Move all terms containing k to the left, all other terms to the right.

Add '-5.5k' to each side of the equation.
5 + 4.5k + -5.5k = 6 + 5.5k + -5.5k

Combine like terms: 4.5k + -5.5k = -1k
5 + -1k = 6 + 5.5k + -5.5k

Combine like terms: 5.5k + -5.5k = 0.0
5 + -1k = 6 + 0.0
5 + -1k = 6

Add '-5' to each side of the equation.
5 + -5 + -1k = 6 + -5

Combine like terms: 5 + -5 = 0
0 + -1k = 6 + -5
-1k = 6 + -5

Combine like terms: 6 + -5 = 1
-1k = 1

Divide each side by '-1'.
k = -1

Simplifying
k = -1

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