3k^2+24k-33=0

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Solution for 3k^2+24k-33=0 equation: 


Simplifying
3k2 + 24k + -33 = 0

Reorder the terms:
-33 + 24k + 3k2 = 0

Solving
-33 + 24k + 3k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-11 + 8k + k2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-11 + 8k + k2)' equal to zero and attempt to solve:

Simplifying
-11 + 8k + k2 = 0

Solving
-11 + 8k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + 8k + 11 + k2 = 0 + 11

Reorder the terms:
-11 + 11 + 8k + k2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 8k + k2 = 0 + 11
8k + k2 = 0 + 11

Combine like terms: 0 + 11 = 11
8k + k2 = 11

The k term is 8k.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8k + 16 + k2 = 11 + 16

Reorder the terms:
16 + 8k + k2 = 11 + 16

Combine like terms: 11 + 16 = 27
16 + 8k + k2 = 27

Factor a perfect square on the left side:
(k + 4)(k + 4) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(k + 4) equal to 5.196152423 and -5.196152423.


Subproblem 1
k + 4 = 5.196152423

Simplifying
k + 4 = 5.196152423

Reorder the terms:
4 + k = 5.196152423

Solving
4 + k = 5.196152423

Solving for variable 'k'.

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

Add '-4' to each side of the equation.
4 + -4 + k = 5.196152423 + -4

Combine like terms: 4 + -4 = 0
0 + k = 5.196152423 + -4
k = 5.196152423 + -4

Combine like terms: 5.196152423 + -4 = 1.196152423
k = 1.196152423

Simplifying
k = 1.196152423


Subproblem 2
k + 4 = -5.196152423

Simplifying
k + 4 = -5.196152423

Reorder the terms:
4 + k = -5.196152423

Solving
4 + k = -5.196152423

Solving for variable 'k'.

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

Add '-4' to each side of the equation.
4 + -4 + k = -5.196152423 + -4

Combine like terms: 4 + -4 = 0
0 + k = -5.196152423 + -4
k = -5.196152423 + -4

Combine like terms: -5.196152423 + -4 = -9.196152423
k = -9.196152423

Simplifying
k = -9.196152423


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {1.196152423, -9.196152423}
Solution
k = {1.196152423, -9.196152423}

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