3k^2-42k-15=0

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Solution for 3k^2-42k-15=0 equation: 


Simplifying
3k2 + -42k + -15 = 0

Reorder the terms:
-15 + -42k + 3k2 = 0

Solving
-15 + -42k + 3k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + -14k + k2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-5 + -14k + k2)' equal to zero and attempt to solve:

Simplifying
-5 + -14k + k2 = 0

Solving
-5 + -14k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -14k + 5 + k2 = 0 + 5

Reorder the terms:
-5 + 5 + -14k + k2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -14k + k2 = 0 + 5
-14k + k2 = 0 + 5

Combine like terms: 0 + 5 = 5
-14k + k2 = 5

The k term is -14k.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14k + 49 + k2 = 5 + 49

Reorder the terms:
49 + -14k + k2 = 5 + 49

Combine like terms: 5 + 49 = 54
49 + -14k + k2 = 54

Factor a perfect square on the left side:
(k + -7)(k + -7) = 54

Calculate the square root of the right side: 7.348469228

Break this problem into two subproblems by setting 
(k + -7) equal to 7.348469228 and -7.348469228.


Subproblem 1
k + -7 = 7.348469228

Simplifying
k + -7 = 7.348469228

Reorder the terms:
-7 + k = 7.348469228

Solving
-7 + k = 7.348469228

Solving for variable 'k'.

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

Add '7' to each side of the equation.
-7 + 7 + k = 7.348469228 + 7

Combine like terms: -7 + 7 = 0
0 + k = 7.348469228 + 7
k = 7.348469228 + 7

Combine like terms: 7.348469228 + 7 = 14.348469228
k = 14.348469228

Simplifying
k = 14.348469228


Subproblem 2
k + -7 = -7.348469228

Simplifying
k + -7 = -7.348469228

Reorder the terms:
-7 + k = -7.348469228

Solving
-7 + k = -7.348469228

Solving for variable 'k'.

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

Add '7' to each side of the equation.
-7 + 7 + k = -7.348469228 + 7

Combine like terms: -7 + 7 = 0
0 + k = -7.348469228 + 7
k = -7.348469228 + 7

Combine like terms: -7.348469228 + 7 = -0.348469228
k = -0.348469228

Simplifying
k = -0.348469228


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {14.348469228, -0.348469228}
Solution
k = {14.348469228, -0.348469228}

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