3k^2+12k+4=0

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Solution for 3k^2+12k+4=0 equation:


Simplifying
3k2 + 12k + 4 = 0

Reorder the terms:
4 + 12k + 3k2 = 0

Solving
4 + 12k + 3k2 = 0

Solving for variable 'k'.

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

Divide each side by '3'.
1.333333333 + 4k + k2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + 4k + -1.333333333 + k2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + 4k + k2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + 4k + k2 = 0 + -1.333333333
4k + k2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
4k + k2 = -1.333333333

The k term is 4k.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4k + 4 + k2 = -1.333333333 + 4

Reorder the terms:
4 + 4k + k2 = -1.333333333 + 4

Combine like terms: -1.333333333 + 4 = 2.666666667
4 + 4k + k2 = 2.666666667

Factor a perfect square on the left side:
(k + 2)(k + 2) = 2.666666667

Calculate the square root of the right side: 1.632993162

Break this problem into two subproblems by setting 
(k + 2) equal to 1.632993162 and -1.632993162.

Subproblem 1

k + 2 = 1.632993162 Simplifying k + 2 = 1.632993162 Reorder the terms: 2 + k = 1.632993162 Solving 2 + k = 1.632993162 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + k = 1.632993162 + -2 Combine like terms: 2 + -2 = 0 0 + k = 1.632993162 + -2 k = 1.632993162 + -2 Combine like terms: 1.632993162 + -2 = -0.367006838 k = -0.367006838 Simplifying k = -0.367006838

Subproblem 2

k + 2 = -1.632993162 Simplifying k + 2 = -1.632993162 Reorder the terms: 2 + k = -1.632993162 Solving 2 + k = -1.632993162 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + k = -1.632993162 + -2 Combine like terms: 2 + -2 = 0 0 + k = -1.632993162 + -2 k = -1.632993162 + -2 Combine like terms: -1.632993162 + -2 = -3.632993162 k = -3.632993162 Simplifying k = -3.632993162

Solution

The solution to the problem is based on the solutions from the subproblems. k = {-0.367006838, -3.632993162}

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