(3k-1)(k+4)=11

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Solution for (3k-1)(k+4)=11 equation:


Simplifying
(3k + -1)(k + 4) = 11

Reorder the terms:
(-1 + 3k)(k + 4) = 11

Reorder the terms:
(-1 + 3k)(4 + k) = 11

Multiply (-1 + 3k) * (4 + k)
(-1(4 + k) + 3k * (4 + k)) = 11
((4 * -1 + k * -1) + 3k * (4 + k)) = 11
((-4 + -1k) + 3k * (4 + k)) = 11
(-4 + -1k + (4 * 3k + k * 3k)) = 11
(-4 + -1k + (12k + 3k2)) = 11

Combine like terms: -1k + 12k = 11k
(-4 + 11k + 3k2) = 11

Solving
-4 + 11k + 3k2 = 11

Solving for variable 'k'.

Reorder the terms:
-4 + -11 + 11k + 3k2 = 11 + -11

Combine like terms: -4 + -11 = -15
-15 + 11k + 3k2 = 11 + -11

Combine like terms: 11 + -11 = 0
-15 + 11k + 3k2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-5 + 3.666666667k + k2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 3.666666667k + 5 + k2 = 0 + 5

Reorder the terms:
-5 + 5 + 3.666666667k + k2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 3.666666667k + k2 = 0 + 5
3.666666667k + k2 = 0 + 5

Combine like terms: 0 + 5 = 5
3.666666667k + k2 = 5

The k term is 3.666666667k.  Take half its coefficient (1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
3.666666667k + 3.361111114 + k2 = 5 + 3.361111114

Reorder the terms:
3.361111114 + 3.666666667k + k2 = 5 + 3.361111114

Combine like terms: 5 + 3.361111114 = 8.361111114
3.361111114 + 3.666666667k + k2 = 8.361111114

Factor a perfect square on the left side:
(k + 1.833333334)(k + 1.833333334) = 8.361111114

Calculate the square root of the right side: 2.891558596

Break this problem into two subproblems by setting 
(k + 1.833333334) equal to 2.891558596 and -2.891558596.

Subproblem 1

k + 1.833333334 = 2.891558596 Simplifying k + 1.833333334 = 2.891558596 Reorder the terms: 1.833333334 + k = 2.891558596 Solving 1.833333334 + k = 2.891558596 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + k = 2.891558596 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + k = 2.891558596 + -1.833333334 k = 2.891558596 + -1.833333334 Combine like terms: 2.891558596 + -1.833333334 = 1.058225262 k = 1.058225262 Simplifying k = 1.058225262

Subproblem 2

k + 1.833333334 = -2.891558596 Simplifying k + 1.833333334 = -2.891558596 Reorder the terms: 1.833333334 + k = -2.891558596 Solving 1.833333334 + k = -2.891558596 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + k = -2.891558596 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + k = -2.891558596 + -1.833333334 k = -2.891558596 + -1.833333334 Combine like terms: -2.891558596 + -1.833333334 = -4.72489193 k = -4.72489193 Simplifying k = -4.72489193

Solution

The solution to the problem is based on the solutions from the subproblems. k = {1.058225262, -4.72489193}

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