-20k^2+34k=3k-27

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Solution for -20k^2+34k=3k-27 equation:


Simplifying
-20k2 + 34k = 3k + -27

Reorder the terms:
34k + -20k2 = 3k + -27

Reorder the terms:
34k + -20k2 = -27 + 3k

Solving
34k + -20k2 = -27 + 3k

Solving for variable 'k'.

Reorder the terms:
27 + 34k + -3k + -20k2 = -27 + 3k + 27 + -3k

Combine like terms: 34k + -3k = 31k
27 + 31k + -20k2 = -27 + 3k + 27 + -3k

Reorder the terms:
27 + 31k + -20k2 = -27 + 27 + 3k + -3k

Combine like terms: -27 + 27 = 0
27 + 31k + -20k2 = 0 + 3k + -3k
27 + 31k + -20k2 = 3k + -3k

Combine like terms: 3k + -3k = 0
27 + 31k + -20k2 = 0

Begin completing the square.  Divide all terms by
-20 the coefficient of the squared term: 

Divide each side by '-20'.
-1.35 + -1.55k + k2 = 0

Move the constant term to the right:

Add '1.35' to each side of the equation.
-1.35 + -1.55k + 1.35 + k2 = 0 + 1.35

Reorder the terms:
-1.35 + 1.35 + -1.55k + k2 = 0 + 1.35

Combine like terms: -1.35 + 1.35 = 0.00
0.00 + -1.55k + k2 = 0 + 1.35
-1.55k + k2 = 0 + 1.35

Combine like terms: 0 + 1.35 = 1.35
-1.55k + k2 = 1.35

The k term is -1.55k.  Take half its coefficient (-0.775).
Square it (0.600625) and add it to both sides.

Add '0.600625' to each side of the equation.
-1.55k + 0.600625 + k2 = 1.35 + 0.600625

Reorder the terms:
0.600625 + -1.55k + k2 = 1.35 + 0.600625

Combine like terms: 1.35 + 0.600625 = 1.950625
0.600625 + -1.55k + k2 = 1.950625

Factor a perfect square on the left side:
(k + -0.775)(k + -0.775) = 1.950625

Calculate the square root of the right side: 1.396647772

Break this problem into two subproblems by setting 
(k + -0.775) equal to 1.396647772 and -1.396647772.

Subproblem 1

k + -0.775 = 1.396647772 Simplifying k + -0.775 = 1.396647772 Reorder the terms: -0.775 + k = 1.396647772 Solving -0.775 + k = 1.396647772 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.775' to each side of the equation. -0.775 + 0.775 + k = 1.396647772 + 0.775 Combine like terms: -0.775 + 0.775 = 0.000 0.000 + k = 1.396647772 + 0.775 k = 1.396647772 + 0.775 Combine like terms: 1.396647772 + 0.775 = 2.171647772 k = 2.171647772 Simplifying k = 2.171647772

Subproblem 2

k + -0.775 = -1.396647772 Simplifying k + -0.775 = -1.396647772 Reorder the terms: -0.775 + k = -1.396647772 Solving -0.775 + k = -1.396647772 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.775' to each side of the equation. -0.775 + 0.775 + k = -1.396647772 + 0.775 Combine like terms: -0.775 + 0.775 = 0.000 0.000 + k = -1.396647772 + 0.775 k = -1.396647772 + 0.775 Combine like terms: -1.396647772 + 0.775 = -0.621647772 k = -0.621647772 Simplifying k = -0.621647772

Solution

The solution to the problem is based on the solutions from the subproblems. k = {2.171647772, -0.621647772}

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