-6x^2-43x+20=0

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Solution for -6x^2-43x+20=0 equation: 


Simplifying
-6x2 + -43x + 20 = 0

Reorder the terms:
20 + -43x + -6x2 = 0

Solving
20 + -43x + -6x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-3.333333333 + 7.166666667x + x2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + 7.166666667x + 3.333333333 + x2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + 7.166666667x + x2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + 7.166666667x + x2 = 0 + 3.333333333
7.166666667x + x2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
7.166666667x + x2 = 3.333333333

The x term is 7.166666667x.  Take half its coefficient (3.583333334).
Square it (12.84027778) and add it to both sides.

Add '12.84027778' to each side of the equation.
7.166666667x + 12.84027778 + x2 = 3.333333333 + 12.84027778

Reorder the terms:
12.84027778 + 7.166666667x + x2 = 3.333333333 + 12.84027778

Combine like terms: 3.333333333 + 12.84027778 = 16.173611113
12.84027778 + 7.166666667x + x2 = 16.173611113

Factor a perfect square on the left side:
(x + 3.583333334)(x + 3.583333334) = 16.173611113

Calculate the square root of the right side: 4.021642838

Break this problem into two subproblems by setting 
(x + 3.583333334) equal to 4.021642838 and -4.021642838.


Subproblem 1
x + 3.583333334 = 4.021642838

Simplifying
x + 3.583333334 = 4.021642838

Reorder the terms:
3.583333334 + x = 4.021642838

Solving
3.583333334 + x = 4.021642838

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3.583333334' to each side of the equation.
3.583333334 + -3.583333334 + x = 4.021642838 + -3.583333334

Combine like terms: 3.583333334 + -3.583333334 = 0.000000000
0.000000000 + x = 4.021642838 + -3.583333334
x = 4.021642838 + -3.583333334

Combine like terms: 4.021642838 + -3.583333334 = 0.438309504
x = 0.438309504

Simplifying
x = 0.438309504


Subproblem 2
x + 3.583333334 = -4.021642838

Simplifying
x + 3.583333334 = -4.021642838

Reorder the terms:
3.583333334 + x = -4.021642838

Solving
3.583333334 + x = -4.021642838

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3.583333334' to each side of the equation.
3.583333334 + -3.583333334 + x = -4.021642838 + -3.583333334

Combine like terms: 3.583333334 + -3.583333334 = 0.000000000
0.000000000 + x = -4.021642838 + -3.583333334
x = -4.021642838 + -3.583333334

Combine like terms: -4.021642838 + -3.583333334 = -7.604976172
x = -7.604976172

Simplifying
x = -7.604976172


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.438309504, -7.604976172}

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