3x^2+11x-8=0

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Solution for 3x^2+11x-8=0 equation: 


Simplifying
3x2 + 11x + -8 = 0

Reorder the terms:
-8 + 11x + 3x2 = 0

Solving
-8 + 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'.
-2.666666667 + 3.666666667x + x2 = 0

Move the constant term to the right:

Add '2.666666667' to each side of the equation.
-2.666666667 + 3.666666667x + 2.666666667 + x2 = 0 + 2.666666667

Reorder the terms:
-2.666666667 + 2.666666667 + 3.666666667x + x2 = 0 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + 3.666666667x + x2 = 0 + 2.666666667
3.666666667x + x2 = 0 + 2.666666667

Combine like terms: 0 + 2.666666667 = 2.666666667
3.666666667x + x2 = 2.666666667

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 = 2.666666667 + 3.361111114

Reorder the terms:
3.361111114 + 3.666666667x + x2 = 2.666666667 + 3.361111114

Combine like terms: 2.666666667 + 3.361111114 = 6.027777781
3.361111114 + 3.666666667x + x2 = 6.027777781

Factor a perfect square on the left side:
(x + 1.833333334)(x + 1.833333334) = 6.027777781

Calculate the square root of the right side: 2.455153311

Break this problem into two subproblems by setting 
(x + 1.833333334) equal to 2.455153311 and -2.455153311.


Subproblem 1
x + 1.833333334 = 2.455153311

Simplifying
x + 1.833333334 = 2.455153311

Reorder the terms:
1.833333334 + x = 2.455153311

Solving
1.833333334 + x = 2.455153311

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 = 2.455153311 + -1.833333334

Combine like terms: 1.833333334 + -1.833333334 = 0.000000000
0.000000000 + x = 2.455153311 + -1.833333334
x = 2.455153311 + -1.833333334

Combine like terms: 2.455153311 + -1.833333334 = 0.621819977
x = 0.621819977

Simplifying
x = 0.621819977


Subproblem 2
x + 1.833333334 = -2.455153311

Simplifying
x + 1.833333334 = -2.455153311

Reorder the terms:
1.833333334 + x = -2.455153311

Solving
1.833333334 + x = -2.455153311

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 = -2.455153311 + -1.833333334

Combine like terms: 1.833333334 + -1.833333334 = 0.000000000
0.000000000 + x = -2.455153311 + -1.833333334
x = -2.455153311 + -1.833333334

Combine like terms: -2.455153311 + -1.833333334 = -4.288486645
x = -4.288486645

Simplifying
x = -4.288486645


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.621819977, -4.288486645}

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