6x*x+25x-32=0

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Solution for 6x*x+25x-32=0 equation: 


Simplifying
6x * x + 25x + -32 = 0

Multiply x * x
6x2 + 25x + -32 = 0

Reorder the terms:
-32 + 25x + 6x2 = 0

Solving
-32 + 25x + 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'.
-5.333333333 + 4.166666667x + x2 = 0

Move the constant term to the right:

Add '5.333333333' to each side of the equation.
-5.333333333 + 4.166666667x + 5.333333333 + x2 = 0 + 5.333333333

Reorder the terms:
-5.333333333 + 5.333333333 + 4.166666667x + x2 = 0 + 5.333333333

Combine like terms: -5.333333333 + 5.333333333 = 0.000000000
0.000000000 + 4.166666667x + x2 = 0 + 5.333333333
4.166666667x + x2 = 0 + 5.333333333

Combine like terms: 0 + 5.333333333 = 5.333333333
4.166666667x + x2 = 5.333333333

The x term is 4.166666667x.  Take half its coefficient (2.083333334).
Square it (4.340277781) and add it to both sides.

Add '4.340277781' to each side of the equation.
4.166666667x + 4.340277781 + x2 = 5.333333333 + 4.340277781

Reorder the terms:
4.340277781 + 4.166666667x + x2 = 5.333333333 + 4.340277781

Combine like terms: 5.333333333 + 4.340277781 = 9.673611114
4.340277781 + 4.166666667x + x2 = 9.673611114

Factor a perfect square on the left side:
(x + 2.083333334)(x + 2.083333334) = 9.673611114

Calculate the square root of the right side: 3.110242935

Break this problem into two subproblems by setting 
(x + 2.083333334) equal to 3.110242935 and -3.110242935.


Subproblem 1
x + 2.083333334 = 3.110242935

Simplifying
x + 2.083333334 = 3.110242935

Reorder the terms:
2.083333334 + x = 3.110242935

Solving
2.083333334 + x = 3.110242935

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2.083333334' to each side of the equation.
2.083333334 + -2.083333334 + x = 3.110242935 + -2.083333334

Combine like terms: 2.083333334 + -2.083333334 = 0.000000000
0.000000000 + x = 3.110242935 + -2.083333334
x = 3.110242935 + -2.083333334

Combine like terms: 3.110242935 + -2.083333334 = 1.026909601
x = 1.026909601

Simplifying
x = 1.026909601


Subproblem 2
x + 2.083333334 = -3.110242935

Simplifying
x + 2.083333334 = -3.110242935

Reorder the terms:
2.083333334 + x = -3.110242935

Solving
2.083333334 + x = -3.110242935

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2.083333334' to each side of the equation.
2.083333334 + -2.083333334 + x = -3.110242935 + -2.083333334

Combine like terms: 2.083333334 + -2.083333334 = 0.000000000
0.000000000 + x = -3.110242935 + -2.083333334
x = -3.110242935 + -2.083333334

Combine like terms: -3.110242935 + -2.083333334 = -5.193576269
x = -5.193576269

Simplifying
x = -5.193576269


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.026909601, -5.193576269}

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