(1.5x^2)+80x-4000=0

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Solution for (1.5x^2)+80x-4000=0 equation: 


Simplifying
(1.5x2) + 80x + -4000 = 0

Reorder the terms:
-4000 + 80x + (1.5x2) = 0

Solving
-4000 + 80x + (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'.
-2666.666667 + 53.33333333x + x2 = 0

Move the constant term to the right:

Add '2666.666667' to each side of the equation.
-2666.666667 + 53.33333333x + 2666.666667 + x2 = 0 + 2666.666667

Reorder the terms:
-2666.666667 + 2666.666667 + 53.33333333x + x2 = 0 + 2666.666667

Combine like terms: -2666.666667 + 2666.666667 = 0.000000
0.000000 + 53.33333333x + x2 = 0 + 2666.666667
53.33333333x + x2 = 0 + 2666.666667

Combine like terms: 0 + 2666.666667 = 2666.666667
53.33333333x + x2 = 2666.666667

The x term is 53.33333333x.  Take half its coefficient (26.66666667).
Square it (711.1111113) and add it to both sides.

Add '711.1111113' to each side of the equation.
53.33333333x + 711.1111113 + x2 = 2666.666667 + 711.1111113

Reorder the terms:
711.1111113 + 53.33333333x + x2 = 2666.666667 + 711.1111113

Combine like terms: 2666.666667 + 711.1111113 = 3377.7777783
711.1111113 + 53.33333333x + x2 = 3377.7777783

Factor a perfect square on the left side:
((x) + 26.66666667)((x) + 26.66666667) = 3377.7777783

Calculate the square root of the right side: 58.118652585

Break this problem into two subproblems by setting 
((x) + 26.66666667) equal to 58.118652585 and -58.118652585.


Subproblem 1
(x) + 26.66666667 = 58.118652585

Simplifying
(x) + 26.66666667 = 58.118652585
x + 26.66666667 = 58.118652585

Reorder the terms:
26.66666667 + x = 58.118652585

Solving
26.66666667 + x = 58.118652585

Solving for variable 'x'.

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

Add '-26.66666667' to each side of the equation.
26.66666667 + -26.66666667 + x = 58.118652585 + -26.66666667

Combine like terms: 26.66666667 + -26.66666667 = 0.00000000
0.00000000 + x = 58.118652585 + -26.66666667
x = 58.118652585 + -26.66666667

Combine like terms: 58.118652585 + -26.66666667 = 31.451985915
x = 31.451985915

Simplifying
x = 31.451985915


Subproblem 2
(x) + 26.66666667 = -58.118652585

Simplifying
(x) + 26.66666667 = -58.118652585
x + 26.66666667 = -58.118652585

Reorder the terms:
26.66666667 + x = -58.118652585

Solving
26.66666667 + x = -58.118652585

Solving for variable 'x'.

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

Add '-26.66666667' to each side of the equation.
26.66666667 + -26.66666667 + x = -58.118652585 + -26.66666667

Combine like terms: 26.66666667 + -26.66666667 = 0.00000000
0.00000000 + x = -58.118652585 + -26.66666667
x = -58.118652585 + -26.66666667

Combine like terms: -58.118652585 + -26.66666667 = -84.785319255
x = -84.785319255

Simplifying
x = -84.785319255


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {31.451985915, -84.785319255}

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