1.5x^2-25x-76=0

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Solution for 1.5x^2-25x-76=0 equation: 


Simplifying
1.5x2 + -25x + -76 = 0

Reorder the terms:
-76 + -25x + 1.5x2 = 0

Solving
-76 + -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'.
-50.66666667 + -16.66666667x + x2 = 0

Move the constant term to the right:

Add '50.66666667' to each side of the equation.
-50.66666667 + -16.66666667x + 50.66666667 + x2 = 0 + 50.66666667

Reorder the terms:
-50.66666667 + 50.66666667 + -16.66666667x + x2 = 0 + 50.66666667

Combine like terms: -50.66666667 + 50.66666667 = 0.00000000
0.00000000 + -16.66666667x + x2 = 0 + 50.66666667
-16.66666667x + x2 = 0 + 50.66666667

Combine like terms: 0 + 50.66666667 = 50.66666667
-16.66666667x + x2 = 50.66666667

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 = 50.66666667 + 69.44444447

Reorder the terms:
69.44444447 + -16.66666667x + x2 = 50.66666667 + 69.44444447

Combine like terms: 50.66666667 + 69.44444447 = 120.11111114
69.44444447 + -16.66666667x + x2 = 120.11111114

Factor a perfect square on the left side:
(x + -8.333333335)(x + -8.333333335) = 120.11111114

Calculate the square root of the right side: 10.959521483

Break this problem into two subproblems by setting 
(x + -8.333333335) equal to 10.959521483 and -10.959521483.


Subproblem 1
x + -8.333333335 = 10.959521483

Simplifying
x + -8.333333335 = 10.959521483

Reorder the terms:
-8.333333335 + x = 10.959521483

Solving
-8.333333335 + x = 10.959521483

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 = 10.959521483 + 8.333333335

Combine like terms: -8.333333335 + 8.333333335 = 0.000000000
0.000000000 + x = 10.959521483 + 8.333333335
x = 10.959521483 + 8.333333335

Combine like terms: 10.959521483 + 8.333333335 = 19.292854818
x = 19.292854818

Simplifying
x = 19.292854818


Subproblem 2
x + -8.333333335 = -10.959521483

Simplifying
x + -8.333333335 = -10.959521483

Reorder the terms:
-8.333333335 + x = -10.959521483

Solving
-8.333333335 + x = -10.959521483

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 = -10.959521483 + 8.333333335

Combine like terms: -8.333333335 + 8.333333335 = 0.000000000
0.000000000 + x = -10.959521483 + 8.333333335
x = -10.959521483 + 8.333333335

Combine like terms: -10.959521483 + 8.333333335 = -2.626188148
x = -2.626188148

Simplifying
x = -2.626188148


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.292854818, -2.626188148}

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