9-12k-4k^2=0

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Solution for 9-12k-4k^2=0 equation:


Simplifying
9 + -12k + -4k2 = 0

Solving
9 + -12k + -4k2 = 0

Solving for variable 'k'.

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-2.25 + 3k + k2 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + 3k + 2.25 + k2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + 3k + k2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + 3k + k2 = 0 + 2.25
3k + k2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
3k + k2 = 2.25

The k term is 3k.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3k + 2.25 + k2 = 2.25 + 2.25

Reorder the terms:
2.25 + 3k + k2 = 2.25 + 2.25

Combine like terms: 2.25 + 2.25 = 4.5
2.25 + 3k + k2 = 4.5

Factor a perfect square on the left side:
(k + 1.5)(k + 1.5) = 4.5

Calculate the square root of the right side: 2.121320344

Break this problem into two subproblems by setting 
(k + 1.5) equal to 2.121320344 and -2.121320344.

Subproblem 1

k + 1.5 = 2.121320344 Simplifying k + 1.5 = 2.121320344 Reorder the terms: 1.5 + k = 2.121320344 Solving 1.5 + k = 2.121320344 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + k = 2.121320344 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + k = 2.121320344 + -1.5 k = 2.121320344 + -1.5 Combine like terms: 2.121320344 + -1.5 = 0.621320344 k = 0.621320344 Simplifying k = 0.621320344

Subproblem 2

k + 1.5 = -2.121320344 Simplifying k + 1.5 = -2.121320344 Reorder the terms: 1.5 + k = -2.121320344 Solving 1.5 + k = -2.121320344 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + k = -2.121320344 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + k = -2.121320344 + -1.5 k = -2.121320344 + -1.5 Combine like terms: -2.121320344 + -1.5 = -3.621320344 k = -3.621320344 Simplifying k = -3.621320344

Solution

The solution to the problem is based on the solutions from the subproblems. k = {0.621320344, -3.621320344}

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