3x^2+11x-25=0

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Solution for 3x^2+11x-25=0 equation: 


Simplifying
3x2 + 11x + -25 = 0

Reorder the terms:
-25 + 11x + 3x2 = 0

Solving
-25 + 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'.
-8.333333333 + 3.666666667x + x2 = 0

Move the constant term to the right:

Add '8.333333333' to each side of the equation.
-8.333333333 + 3.666666667x + 8.333333333 + x2 = 0 + 8.333333333

Reorder the terms:
-8.333333333 + 8.333333333 + 3.666666667x + x2 = 0 + 8.333333333

Combine like terms: -8.333333333 + 8.333333333 = 0.000000000
0.000000000 + 3.666666667x + x2 = 0 + 8.333333333
3.666666667x + x2 = 0 + 8.333333333

Combine like terms: 0 + 8.333333333 = 8.333333333
3.666666667x + x2 = 8.333333333

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 = 8.333333333 + 3.361111114

Reorder the terms:
3.361111114 + 3.666666667x + x2 = 8.333333333 + 3.361111114

Combine like terms: 8.333333333 + 3.361111114 = 11.694444447
3.361111114 + 3.666666667x + x2 = 11.694444447

Factor a perfect square on the left side:
(x + 1.833333334)(x + 1.833333334) = 11.694444447

Calculate the square root of the right side: 3.419714088

Break this problem into two subproblems by setting 
(x + 1.833333334) equal to 3.419714088 and -3.419714088.


Subproblem 1
x + 1.833333334 = 3.419714088

Simplifying
x + 1.833333334 = 3.419714088

Reorder the terms:
1.833333334 + x = 3.419714088

Solving
1.833333334 + x = 3.419714088

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 = 3.419714088 + -1.833333334

Combine like terms: 1.833333334 + -1.833333334 = 0.000000000
0.000000000 + x = 3.419714088 + -1.833333334
x = 3.419714088 + -1.833333334

Combine like terms: 3.419714088 + -1.833333334 = 1.586380754
x = 1.586380754

Simplifying
x = 1.586380754


Subproblem 2
x + 1.833333334 = -3.419714088

Simplifying
x + 1.833333334 = -3.419714088

Reorder the terms:
1.833333334 + x = -3.419714088

Solving
1.833333334 + x = -3.419714088

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 = -3.419714088 + -1.833333334

Combine like terms: 1.833333334 + -1.833333334 = 0.000000000
0.000000000 + x = -3.419714088 + -1.833333334
x = -3.419714088 + -1.833333334

Combine like terms: -3.419714088 + -1.833333334 = -5.253047422
x = -5.253047422

Simplifying
x = -5.253047422


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.586380754, -5.253047422}

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