1.5x^2+7.5x-100=0

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Solution for 1.5x^2+7.5x-100=0 equation: 


Simplifying
1.5x2 + 7.5x + -100 = 0

Reorder the terms:
-100 + 7.5x + 1.5x2 = 0

Solving
-100 + 7.5x + 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 + 5x + x2 = 0

Move the constant term to the right:

Add '66.66666667' to each side of the equation.
-66.66666667 + 5x + 66.66666667 + x2 = 0 + 66.66666667

Reorder the terms:
-66.66666667 + 66.66666667 + 5x + x2 = 0 + 66.66666667

Combine like terms: -66.66666667 + 66.66666667 = 0.00000000
0.00000000 + 5x + x2 = 0 + 66.66666667
5x + x2 = 0 + 66.66666667

Combine like terms: 0 + 66.66666667 = 66.66666667
5x + x2 = 66.66666667

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 66.66666667 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 66.66666667 + 6.25

Combine like terms: 66.66666667 + 6.25 = 72.91666667
6.25 + 5x + x2 = 72.91666667

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 72.91666667

Calculate the square root of the right side: 8.539125638

Break this problem into two subproblems by setting 
(x + 2.5) equal to 8.539125638 and -8.539125638.


Subproblem 1
x + 2.5 = 8.539125638

Simplifying
x + 2.5 = 8.539125638

Reorder the terms:
2.5 + x = 8.539125638

Solving
2.5 + x = 8.539125638

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 8.539125638 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 8.539125638 + -2.5
x = 8.539125638 + -2.5

Combine like terms: 8.539125638 + -2.5 = 6.039125638
x = 6.039125638

Simplifying
x = 6.039125638


Subproblem 2
x + 2.5 = -8.539125638

Simplifying
x + 2.5 = -8.539125638

Reorder the terms:
2.5 + x = -8.539125638

Solving
2.5 + x = -8.539125638

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -8.539125638 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -8.539125638 + -2.5
x = -8.539125638 + -2.5

Combine like terms: -8.539125638 + -2.5 = -11.039125638
x = -11.039125638

Simplifying
x = -11.039125638


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.039125638, -11.039125638}

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