21k^2-37k=12

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Solution for 21k^2-37k=12 equation:


Simplifying
21k2 + -37k = 12

Reorder the terms:
-37k + 21k2 = 12

Solving
-37k + 21k2 = 12

Solving for variable 'k'.

Reorder the terms:
-12 + -37k + 21k2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + -37k + 21k2 = 0

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

Divide each side by '21'.
-0.5714285714 + -1.761904762k + k2 = 0

Move the constant term to the right:

Add '0.5714285714' to each side of the equation.
-0.5714285714 + -1.761904762k + 0.5714285714 + k2 = 0 + 0.5714285714

Reorder the terms:
-0.5714285714 + 0.5714285714 + -1.761904762k + k2 = 0 + 0.5714285714

Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000
0.0000000000 + -1.761904762k + k2 = 0 + 0.5714285714
-1.761904762k + k2 = 0 + 0.5714285714

Combine like terms: 0 + 0.5714285714 = 0.5714285714
-1.761904762k + k2 = 0.5714285714

The k term is -1.761904762k.  Take half its coefficient (-0.880952381).
Square it (0.7760770976) and add it to both sides.

Add '0.7760770976' to each side of the equation.
-1.761904762k + 0.7760770976 + k2 = 0.5714285714 + 0.7760770976

Reorder the terms:
0.7760770976 + -1.761904762k + k2 = 0.5714285714 + 0.7760770976

Combine like terms: 0.5714285714 + 0.7760770976 = 1.347505669
0.7760770976 + -1.761904762k + k2 = 1.347505669

Factor a perfect square on the left side:
(k + -0.880952381)(k + -0.880952381) = 1.347505669

Calculate the square root of the right side: 1.160821118

Break this problem into two subproblems by setting 
(k + -0.880952381) equal to 1.160821118 and -1.160821118.

Subproblem 1

k + -0.880952381 = 1.160821118 Simplifying k + -0.880952381 = 1.160821118 Reorder the terms: -0.880952381 + k = 1.160821118 Solving -0.880952381 + k = 1.160821118 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.880952381' to each side of the equation. -0.880952381 + 0.880952381 + k = 1.160821118 + 0.880952381 Combine like terms: -0.880952381 + 0.880952381 = 0.000000000 0.000000000 + k = 1.160821118 + 0.880952381 k = 1.160821118 + 0.880952381 Combine like terms: 1.160821118 + 0.880952381 = 2.041773499 k = 2.041773499 Simplifying k = 2.041773499

Subproblem 2

k + -0.880952381 = -1.160821118 Simplifying k + -0.880952381 = -1.160821118 Reorder the terms: -0.880952381 + k = -1.160821118 Solving -0.880952381 + k = -1.160821118 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.880952381' to each side of the equation. -0.880952381 + 0.880952381 + k = -1.160821118 + 0.880952381 Combine like terms: -0.880952381 + 0.880952381 = 0.000000000 0.000000000 + k = -1.160821118 + 0.880952381 k = -1.160821118 + 0.880952381 Combine like terms: -1.160821118 + 0.880952381 = -0.279868737 k = -0.279868737 Simplifying k = -0.279868737

Solution

The solution to the problem is based on the solutions from the subproblems. k = {2.041773499, -0.279868737}

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