6x^2+37x-6=0

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Solution for 6x^2+37x-6=0 equation:


Simplifying
6x2 + 37x + -6 = 0

Reorder the terms:
-6 + 37x + 6x2 = 0

Solving
-6 + 37x + 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'.
-1 + 6.166666667x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 6.166666667x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 6.166666667x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 6.166666667x + x2 = 0 + 1
6.166666667x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
6.166666667x + x2 = 1

The x term is 6.166666667x.  Take half its coefficient (3.083333334).
Square it (9.506944449) and add it to both sides.

Add '9.506944449' to each side of the equation.
6.166666667x + 9.506944449 + x2 = 1 + 9.506944449

Reorder the terms:
9.506944449 + 6.166666667x + x2 = 1 + 9.506944449

Combine like terms: 1 + 9.506944449 = 10.506944449
9.506944449 + 6.166666667x + x2 = 10.506944449

Factor a perfect square on the left side:
(x + 3.083333334)(x + 3.083333334) = 10.506944449

Calculate the square root of the right side: 3.241441724

Break this problem into two subproblems by setting 
(x + 3.083333334) equal to 3.241441724 and -3.241441724.

Subproblem 1

x + 3.083333334 = 3.241441724 Simplifying x + 3.083333334 = 3.241441724 Reorder the terms: 3.083333334 + x = 3.241441724 Solving 3.083333334 + x = 3.241441724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.083333334' to each side of the equation. 3.083333334 + -3.083333334 + x = 3.241441724 + -3.083333334 Combine like terms: 3.083333334 + -3.083333334 = 0.000000000 0.000000000 + x = 3.241441724 + -3.083333334 x = 3.241441724 + -3.083333334 Combine like terms: 3.241441724 + -3.083333334 = 0.15810839 x = 0.15810839 Simplifying x = 0.15810839

Subproblem 2

x + 3.083333334 = -3.241441724 Simplifying x + 3.083333334 = -3.241441724 Reorder the terms: 3.083333334 + x = -3.241441724 Solving 3.083333334 + x = -3.241441724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.083333334' to each side of the equation. 3.083333334 + -3.083333334 + x = -3.241441724 + -3.083333334 Combine like terms: 3.083333334 + -3.083333334 = 0.000000000 0.000000000 + x = -3.241441724 + -3.083333334 x = -3.241441724 + -3.083333334 Combine like terms: -3.241441724 + -3.083333334 = -6.324775058 x = -6.324775058 Simplifying x = -6.324775058

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.15810839, -6.324775058}

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