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

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

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

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

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

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

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

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

Combine like terms: 11 + -1 = 10
5 + 4.5k + -0.5k2 = 0.5(1 + k)(10 + -1k)

Multiply (1 + k) * (10 + -1k)
5 + 4.5k + -0.5k2 = 0.5(1(10 + -1k) + k(10 + -1k))
5 + 4.5k + -0.5k2 = 0.5((10 * 1 + -1k * 1) + k(10 + -1k))
5 + 4.5k + -0.5k2 = 0.5((10 + -1k) + k(10 + -1k))
5 + 4.5k + -0.5k2 = 0.5(10 + -1k + (10 * k + -1k * k))
5 + 4.5k + -0.5k2 = 0.5(10 + -1k + (10k + -1k2))

Combine like terms: -1k + 10k = 9k
5 + 4.5k + -0.5k2 = 0.5(10 + 9k + -1k2)
5 + 4.5k + -0.5k2 = (10 * 0.5 + 9k * 0.5 + -1k2 * 0.5)
5 + 4.5k + -0.5k2 = (5 + 4.5k + -0.5k2)

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

Reorder the terms:
5 + -5 + 4.5k + -0.5k2 = 5 + 4.5k + -5 + -0.5k2

Combine like terms: 5 + -5 = 0
0 + 4.5k + -0.5k2 = 5 + 4.5k + -5 + -0.5k2
4.5k + -0.5k2 = 5 + 4.5k + -5 + -0.5k2

Reorder the terms:
4.5k + -0.5k2 = 5 + -5 + 4.5k + -0.5k2

Combine like terms: 5 + -5 = 0
4.5k + -0.5k2 = 0 + 4.5k + -0.5k2
4.5k + -0.5k2 = 4.5k + -0.5k2

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

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

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

Add '0.5k2' to each side of the equation.
-0.5k2 + 0.5k2 = -0.5k2 + 0.5k2

Combine like terms: -0.5k2 + 0.5k2 = 0.0
0.0 = -0.5k2 + 0.5k2

Combine like terms: -0.5k2 + 0.5k2 = 0.0
0.0 = 0.0

Solving
0.0 = 0.0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.

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