3x^2-11x-37=0

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Solution for 3x^2-11x-37=0 equation:


Simplifying
3x2 + -11x + -37 = 0

Reorder the terms:
-37 + -11x + 3x2 = 0

Solving
-37 + -11x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-12.33333333 + -3.666666667x + x2 = 0

Move the constant term to the right:

Add '12.33333333' to each side of the equation.
-12.33333333 + -3.666666667x + 12.33333333 + x2 = 0 + 12.33333333

Reorder the terms:
-12.33333333 + 12.33333333 + -3.666666667x + x2 = 0 + 12.33333333

Combine like terms: -12.33333333 + 12.33333333 = 0.00000000
0.00000000 + -3.666666667x + x2 = 0 + 12.33333333
-3.666666667x + x2 = 0 + 12.33333333

Combine like terms: 0 + 12.33333333 = 12.33333333
-3.666666667x + x2 = 12.33333333

The x term is -3.666666667x.  Take half its coefficient (-1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
-3.666666667x + 3.361111114 + x2 = 12.33333333 + 3.361111114

Reorder the terms:
3.361111114 + -3.666666667x + x2 = 12.33333333 + 3.361111114

Combine like terms: 12.33333333 + 3.361111114 = 15.694444444
3.361111114 + -3.666666667x + x2 = 15.694444444

Factor a perfect square on the left side:
(x + -1.833333334)(x + -1.833333334) = 15.694444444

Calculate the square root of the right side: 3.961621441

Break this problem into two subproblems by setting 
(x + -1.833333334) equal to 3.961621441 and -3.961621441.

Subproblem 1

x + -1.833333334 = 3.961621441 Simplifying x + -1.833333334 = 3.961621441 Reorder the terms: -1.833333334 + x = 3.961621441 Solving -1.833333334 + x = 3.961621441 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = 3.961621441 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = 3.961621441 + 1.833333334 x = 3.961621441 + 1.833333334 Combine like terms: 3.961621441 + 1.833333334 = 5.794954775 x = 5.794954775 Simplifying x = 5.794954775

Subproblem 2

x + -1.833333334 = -3.961621441 Simplifying x + -1.833333334 = -3.961621441 Reorder the terms: -1.833333334 + x = -3.961621441 Solving -1.833333334 + x = -3.961621441 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = -3.961621441 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = -3.961621441 + 1.833333334 x = -3.961621441 + 1.833333334 Combine like terms: -3.961621441 + 1.833333334 = -2.128288107 x = -2.128288107 Simplifying x = -2.128288107

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.794954775, -2.128288107}

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