-1.5x^2-34x-100=0

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Solution for -1.5x^2-34x-100=0 equation: 


Simplifying
-1.5x2 + -34x + -100 = 0

Reorder the terms:
-100 + -34x + -1.5x2 = 0

Solving
-100 + -34x + -1.5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1.5 the coefficient of the squared term: 

Divide each side by '-1.5'.
66.66666667 + 22.66666667x + x2 = 0

Move the constant term to the right:

Add '-66.66666667' to each side of the equation.
66.66666667 + 22.66666667x + -66.66666667 + x2 = 0 + -66.66666667

Reorder the terms:
66.66666667 + -66.66666667 + 22.66666667x + x2 = 0 + -66.66666667

Combine like terms: 66.66666667 + -66.66666667 = 0.00000000
0.00000000 + 22.66666667x + x2 = 0 + -66.66666667
22.66666667x + x2 = 0 + -66.66666667

Combine like terms: 0 + -66.66666667 = -66.66666667
22.66666667x + x2 = -66.66666667

The x term is 22.66666667x.  Take half its coefficient (11.33333334).
Square it (128.4444446) and add it to both sides.

Add '128.4444446' to each side of the equation.
22.66666667x + 128.4444446 + x2 = -66.66666667 + 128.4444446

Reorder the terms:
128.4444446 + 22.66666667x + x2 = -66.66666667 + 128.4444446

Combine like terms: -66.66666667 + 128.4444446 = 61.77777793
128.4444446 + 22.66666667x + x2 = 61.77777793

Factor a perfect square on the left side:
(x + 11.33333334)(x + 11.33333334) = 61.77777793

Calculate the square root of the right side: 7.859884091

Break this problem into two subproblems by setting 
(x + 11.33333334) equal to 7.859884091 and -7.859884091.


Subproblem 1
x + 11.33333334 = 7.859884091

Simplifying
x + 11.33333334 = 7.859884091

Reorder the terms:
11.33333334 + x = 7.859884091

Solving
11.33333334 + x = 7.859884091

Solving for variable 'x'.

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

Add '-11.33333334' to each side of the equation.
11.33333334 + -11.33333334 + x = 7.859884091 + -11.33333334

Combine like terms: 11.33333334 + -11.33333334 = 0.00000000
0.00000000 + x = 7.859884091 + -11.33333334
x = 7.859884091 + -11.33333334

Combine like terms: 7.859884091 + -11.33333334 = -3.473449249
x = -3.473449249

Simplifying
x = -3.473449249


Subproblem 2
x + 11.33333334 = -7.859884091

Simplifying
x + 11.33333334 = -7.859884091

Reorder the terms:
11.33333334 + x = -7.859884091

Solving
11.33333334 + x = -7.859884091

Solving for variable 'x'.

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

Add '-11.33333334' to each side of the equation.
11.33333334 + -11.33333334 + x = -7.859884091 + -11.33333334

Combine like terms: 11.33333334 + -11.33333334 = 0.00000000
0.00000000 + x = -7.859884091 + -11.33333334
x = -7.859884091 + -11.33333334

Combine like terms: -7.859884091 + -11.33333334 = -19.193217431
x = -19.193217431

Simplifying
x = -19.193217431


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.473449249, -19.193217431}

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