3x^2+11x-17=0

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Solution for 3x^2+11x-17=0 equation: 


Simplifying
3x2 + 11x + -17 = 0

Reorder the terms:
-17 + 11x + 3x2 = 0

Solving
-17 + 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'.
-5.666666667 + 3.666666667x + x2 = 0

Move the constant term to the right:

Add '5.666666667' to each side of the equation.
-5.666666667 + 3.666666667x + 5.666666667 + x2 = 0 + 5.666666667

Reorder the terms:
-5.666666667 + 5.666666667 + 3.666666667x + x2 = 0 + 5.666666667

Combine like terms: -5.666666667 + 5.666666667 = 0.000000000
0.000000000 + 3.666666667x + x2 = 0 + 5.666666667
3.666666667x + x2 = 0 + 5.666666667

Combine like terms: 0 + 5.666666667 = 5.666666667
3.666666667x + x2 = 5.666666667

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 = 5.666666667 + 3.361111114

Reorder the terms:
3.361111114 + 3.666666667x + x2 = 5.666666667 + 3.361111114

Combine like terms: 5.666666667 + 3.361111114 = 9.027777781
3.361111114 + 3.666666667x + x2 = 9.027777781

Factor a perfect square on the left side:
(x + 1.833333334)(x + 1.833333334) = 9.027777781

Calculate the square root of the right side: 3.004626063

Break this problem into two subproblems by setting 
(x + 1.833333334) equal to 3.004626063 and -3.004626063.


Subproblem 1
x + 1.833333334 = 3.004626063

Simplifying
x + 1.833333334 = 3.004626063

Reorder the terms:
1.833333334 + x = 3.004626063

Solving
1.833333334 + x = 3.004626063

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 = 3.004626063 + -1.833333334

Combine like terms: 1.833333334 + -1.833333334 = 0.000000000
0.000000000 + x = 3.004626063 + -1.833333334
x = 3.004626063 + -1.833333334

Combine like terms: 3.004626063 + -1.833333334 = 1.171292729
x = 1.171292729

Simplifying
x = 1.171292729


Subproblem 2
x + 1.833333334 = -3.004626063

Simplifying
x + 1.833333334 = -3.004626063

Reorder the terms:
1.833333334 + x = -3.004626063

Solving
1.833333334 + x = -3.004626063

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 = -3.004626063 + -1.833333334

Combine like terms: 1.833333334 + -1.833333334 = 0.000000000
0.000000000 + x = -3.004626063 + -1.833333334
x = -3.004626063 + -1.833333334

Combine like terms: -3.004626063 + -1.833333334 = -4.837959397
x = -4.837959397

Simplifying
x = -4.837959397


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.171292729, -4.837959397}

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