.3k^2-6k=2.4

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Solution for .3k^2-6k=2.4 equation:


Simplifying
0.3k2 + -6k = 2.4

Reorder the terms:
-6k + 0.3k2 = 2.4

Solving
-6k + 0.3k2 = 2.4

Solving for variable 'k'.

Reorder the terms:
-2.4 + -6k + 0.3k2 = 2.4 + -2.4

Combine like terms: 2.4 + -2.4 = 0.0
-2.4 + -6k + 0.3k2 = 0.0

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

Divide each side by '0.3'.
-8 + -20k + k2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -20k + 8 + k2 = 0 + 8

Reorder the terms:
-8 + 8 + -20k + k2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -20k + k2 = 0 + 8
-20k + k2 = 0 + 8

Combine like terms: 0 + 8 = 8
-20k + k2 = 8

The k term is -20k.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20k + 100 + k2 = 8 + 100

Reorder the terms:
100 + -20k + k2 = 8 + 100

Combine like terms: 8 + 100 = 108
100 + -20k + k2 = 108

Factor a perfect square on the left side:
(k + -10)(k + -10) = 108

Calculate the square root of the right side: 10.392304845

Break this problem into two subproblems by setting 
(k + -10) equal to 10.392304845 and -10.392304845.

Subproblem 1

k + -10 = 10.392304845 Simplifying k + -10 = 10.392304845 Reorder the terms: -10 + k = 10.392304845 Solving -10 + k = 10.392304845 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + k = 10.392304845 + 10 Combine like terms: -10 + 10 = 0 0 + k = 10.392304845 + 10 k = 10.392304845 + 10 Combine like terms: 10.392304845 + 10 = 20.392304845 k = 20.392304845 Simplifying k = 20.392304845

Subproblem 2

k + -10 = -10.392304845 Simplifying k + -10 = -10.392304845 Reorder the terms: -10 + k = -10.392304845 Solving -10 + k = -10.392304845 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + k = -10.392304845 + 10 Combine like terms: -10 + 10 = 0 0 + k = -10.392304845 + 10 k = -10.392304845 + 10 Combine like terms: -10.392304845 + 10 = -0.392304845 k = -0.392304845 Simplifying k = -0.392304845

Solution

The solution to the problem is based on the solutions from the subproblems. k = {20.392304845, -0.392304845}

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