6x^2-13x-4=0

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Solution for 6x^2-13x-4=0 equation:


Simplifying
6x2 + -13x + -4 = 0

Reorder the terms:
-4 + -13x + 6x2 = 0

Solving
-4 + -13x + 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'.
-0.6666666667 + -2.166666667x + x2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + -2.166666667x + 0.6666666667 + x2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + -2.166666667x + x2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + -2.166666667x + x2 = 0 + 0.6666666667
-2.166666667x + x2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
-2.166666667x + x2 = 0.6666666667

The x term is -2.166666667x.  Take half its coefficient (-1.083333334).
Square it (1.173611113) and add it to both sides.

Add '1.173611113' to each side of the equation.
-2.166666667x + 1.173611113 + x2 = 0.6666666667 + 1.173611113

Reorder the terms:
1.173611113 + -2.166666667x + x2 = 0.6666666667 + 1.173611113

Combine like terms: 0.6666666667 + 1.173611113 = 1.8402777797
1.173611113 + -2.166666667x + x2 = 1.8402777797

Factor a perfect square on the left side:
(x + -1.083333334)(x + -1.083333334) = 1.8402777797

Calculate the square root of the right side: 1.356568384

Break this problem into two subproblems by setting 
(x + -1.083333334) equal to 1.356568384 and -1.356568384.

Subproblem 1

x + -1.083333334 = 1.356568384 Simplifying x + -1.083333334 = 1.356568384 Reorder the terms: -1.083333334 + x = 1.356568384 Solving -1.083333334 + x = 1.356568384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.083333334' to each side of the equation. -1.083333334 + 1.083333334 + x = 1.356568384 + 1.083333334 Combine like terms: -1.083333334 + 1.083333334 = 0.000000000 0.000000000 + x = 1.356568384 + 1.083333334 x = 1.356568384 + 1.083333334 Combine like terms: 1.356568384 + 1.083333334 = 2.439901718 x = 2.439901718 Simplifying x = 2.439901718

Subproblem 2

x + -1.083333334 = -1.356568384 Simplifying x + -1.083333334 = -1.356568384 Reorder the terms: -1.083333334 + x = -1.356568384 Solving -1.083333334 + x = -1.356568384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.083333334' to each side of the equation. -1.083333334 + 1.083333334 + x = -1.356568384 + 1.083333334 Combine like terms: -1.083333334 + 1.083333334 = 0.000000000 0.000000000 + x = -1.356568384 + 1.083333334 x = -1.356568384 + 1.083333334 Combine like terms: -1.356568384 + 1.083333334 = -0.27323505 x = -0.27323505 Simplifying x = -0.27323505

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.439901718, -0.27323505}

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