6x^2+13x-38=0

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Solution for 6x^2+13x-38=0 equation: 


Simplifying
6x2 + 13x + -38 = 0

Reorder the terms:
-38 + 13x + 6x2 = 0

Solving
-38 + 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'.
-6.333333333 + 2.166666667x + x2 = 0

Move the constant term to the right:

Add '6.333333333' to each side of the equation.
-6.333333333 + 2.166666667x + 6.333333333 + x2 = 0 + 6.333333333

Reorder the terms:
-6.333333333 + 6.333333333 + 2.166666667x + x2 = 0 + 6.333333333

Combine like terms: -6.333333333 + 6.333333333 = 0.000000000
0.000000000 + 2.166666667x + x2 = 0 + 6.333333333
2.166666667x + x2 = 0 + 6.333333333

Combine like terms: 0 + 6.333333333 = 6.333333333
2.166666667x + x2 = 6.333333333

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 = 6.333333333 + 1.173611113

Reorder the terms:
1.173611113 + 2.166666667x + x2 = 6.333333333 + 1.173611113

Combine like terms: 6.333333333 + 1.173611113 = 7.506944446
1.173611113 + 2.166666667x + x2 = 7.506944446

Factor a perfect square on the left side:
(x + 1.083333334)(x + 1.083333334) = 7.506944446

Calculate the square root of the right side: 2.739880371

Break this problem into two subproblems by setting 
(x + 1.083333334) equal to 2.739880371 and -2.739880371.


Subproblem 1
x + 1.083333334 = 2.739880371

Simplifying
x + 1.083333334 = 2.739880371

Reorder the terms:
1.083333334 + x = 2.739880371

Solving
1.083333334 + x = 2.739880371

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 = 2.739880371 + -1.083333334

Combine like terms: 1.083333334 + -1.083333334 = 0.000000000
0.000000000 + x = 2.739880371 + -1.083333334
x = 2.739880371 + -1.083333334

Combine like terms: 2.739880371 + -1.083333334 = 1.656547037
x = 1.656547037

Simplifying
x = 1.656547037


Subproblem 2
x + 1.083333334 = -2.739880371

Simplifying
x + 1.083333334 = -2.739880371

Reorder the terms:
1.083333334 + x = -2.739880371

Solving
1.083333334 + x = -2.739880371

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 = -2.739880371 + -1.083333334

Combine like terms: 1.083333334 + -1.083333334 = 0.000000000
0.000000000 + x = -2.739880371 + -1.083333334
x = -2.739880371 + -1.083333334

Combine like terms: -2.739880371 + -1.083333334 = -3.823213705
x = -3.823213705

Simplifying
x = -3.823213705


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.656547037, -3.823213705}

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