1.5x^2-25x-37.5=0

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Solution for 1.5x^2-25x-37.5=0 equation: 


Simplifying
1.5x2 + -25x + -37.5 = 0

Reorder the terms:
-37.5 + -25x + 1.5x2 = 0

Solving
-37.5 + -25x + 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'.
-25 + -16.66666667x + x2 = 0

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + -16.66666667x + 25 + x2 = 0 + 25

Reorder the terms:
-25 + 25 + -16.66666667x + x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -16.66666667x + x2 = 0 + 25
-16.66666667x + x2 = 0 + 25

Combine like terms: 0 + 25 = 25
-16.66666667x + x2 = 25

The x term is -16.66666667x.  Take half its coefficient (-8.333333335).
Square it (69.44444447) and add it to both sides.

Add '69.44444447' to each side of the equation.
-16.66666667x + 69.44444447 + x2 = 25 + 69.44444447

Reorder the terms:
69.44444447 + -16.66666667x + x2 = 25 + 69.44444447

Combine like terms: 25 + 69.44444447 = 94.44444447
69.44444447 + -16.66666667x + x2 = 94.44444447

Factor a perfect square on the left side:
(x + -8.333333335)(x + -8.333333335) = 94.44444447

Calculate the square root of the right side: 9.718253159

Break this problem into two subproblems by setting 
(x + -8.333333335) equal to 9.718253159 and -9.718253159.


Subproblem 1
x + -8.333333335 = 9.718253159

Simplifying
x + -8.333333335 = 9.718253159

Reorder the terms:
-8.333333335 + x = 9.718253159

Solving
-8.333333335 + x = 9.718253159

Solving for variable 'x'.

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

Add '8.333333335' to each side of the equation.
-8.333333335 + 8.333333335 + x = 9.718253159 + 8.333333335

Combine like terms: -8.333333335 + 8.333333335 = 0.000000000
0.000000000 + x = 9.718253159 + 8.333333335
x = 9.718253159 + 8.333333335

Combine like terms: 9.718253159 + 8.333333335 = 18.051586494
x = 18.051586494

Simplifying
x = 18.051586494


Subproblem 2
x + -8.333333335 = -9.718253159

Simplifying
x + -8.333333335 = -9.718253159

Reorder the terms:
-8.333333335 + x = -9.718253159

Solving
-8.333333335 + x = -9.718253159

Solving for variable 'x'.

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

Add '8.333333335' to each side of the equation.
-8.333333335 + 8.333333335 + x = -9.718253159 + 8.333333335

Combine like terms: -8.333333335 + 8.333333335 = 0.000000000
0.000000000 + x = -9.718253159 + 8.333333335
x = -9.718253159 + 8.333333335

Combine like terms: -9.718253159 + 8.333333335 = -1.384919824
x = -1.384919824

Simplifying
x = -1.384919824


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.051586494, -1.384919824}

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