-1.5x^2-38x-100=0

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Solution for -1.5x^2-38x-100=0 equation: 


Simplifying
-1.5x2 + -38x + -100 = 0

Reorder the terms:
-100 + -38x + -1.5x2 = 0

Solving
-100 + -38x + -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 + 25.33333333x + x2 = 0

Move the constant term to the right:

Add '-66.66666667' to each side of the equation.
66.66666667 + 25.33333333x + -66.66666667 + x2 = 0 + -66.66666667

Reorder the terms:
66.66666667 + -66.66666667 + 25.33333333x + x2 = 0 + -66.66666667

Combine like terms: 66.66666667 + -66.66666667 = 0.00000000
0.00000000 + 25.33333333x + x2 = 0 + -66.66666667
25.33333333x + x2 = 0 + -66.66666667

Combine like terms: 0 + -66.66666667 = -66.66666667
25.33333333x + x2 = -66.66666667

The x term is 25.33333333x.  Take half its coefficient (12.66666667).
Square it (160.4444445) and add it to both sides.

Add '160.4444445' to each side of the equation.
25.33333333x + 160.4444445 + x2 = -66.66666667 + 160.4444445

Reorder the terms:
160.4444445 + 25.33333333x + x2 = -66.66666667 + 160.4444445

Combine like terms: -66.66666667 + 160.4444445 = 93.77777783
160.4444445 + 25.33333333x + x2 = 93.77777783

Factor a perfect square on the left side:
(x + 12.66666667)(x + 12.66666667) = 93.77777783

Calculate the square root of the right side: 9.6838927

Break this problem into two subproblems by setting 
(x + 12.66666667) equal to 9.6838927 and -9.6838927.


Subproblem 1
x + 12.66666667 = 9.6838927

Simplifying
x + 12.66666667 = 9.6838927

Reorder the terms:
12.66666667 + x = 9.6838927

Solving
12.66666667 + x = 9.6838927

Solving for variable 'x'.

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

Add '-12.66666667' to each side of the equation.
12.66666667 + -12.66666667 + x = 9.6838927 + -12.66666667

Combine like terms: 12.66666667 + -12.66666667 = 0.00000000
0.00000000 + x = 9.6838927 + -12.66666667
x = 9.6838927 + -12.66666667

Combine like terms: 9.6838927 + -12.66666667 = -2.98277397
x = -2.98277397

Simplifying
x = -2.98277397


Subproblem 2
x + 12.66666667 = -9.6838927

Simplifying
x + 12.66666667 = -9.6838927

Reorder the terms:
12.66666667 + x = -9.6838927

Solving
12.66666667 + x = -9.6838927

Solving for variable 'x'.

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

Add '-12.66666667' to each side of the equation.
12.66666667 + -12.66666667 + x = -9.6838927 + -12.66666667

Combine like terms: 12.66666667 + -12.66666667 = 0.00000000
0.00000000 + x = -9.6838927 + -12.66666667
x = -9.6838927 + -12.66666667

Combine like terms: -9.6838927 + -12.66666667 = -22.35055937
x = -22.35055937

Simplifying
x = -22.35055937


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.98277397, -22.35055937}

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