-3.5x^2+3775x-135732.5=650000

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Solution for -3.5x^2+3775x-135732.5=650000 equation:


Simplifying
-3.5x2 + 3775x + -135732.5 = 650000

Reorder the terms:
-135732.5 + 3775x + -3.5x2 = 650000

Solving
-135732.5 + 3775x + -3.5x2 = 650000

Solving for variable 'x'.

Reorder the terms:
-135732.5 + -650000 + 3775x + -3.5x2 = 650000 + -650000

Combine like terms: -135732.5 + -650000 = -785732.5
-785732.5 + 3775x + -3.5x2 = 650000 + -650000

Combine like terms: 650000 + -650000 = 0
-785732.5 + 3775x + -3.5x2 = 0

Begin completing the square.  Divide all terms by
-3.5 the coefficient of the squared term: 

Divide each side by '-3.5'.
224495 + -1078.571429x + x2 = 0

Move the constant term to the right:

Add '-224495' to each side of the equation.
224495 + -1078.571429x + -224495 + x2 = 0 + -224495

Reorder the terms:
224495 + -224495 + -1078.571429x + x2 = 0 + -224495

Combine like terms: 224495 + -224495 = 0
0 + -1078.571429x + x2 = 0 + -224495
-1078.571429x + x2 = 0 + -224495

Combine like terms: 0 + -224495 = -224495
-1078.571429x + x2 = -224495

The x term is -1078.571429x.  Take half its coefficient (-539.2857145).
Square it (290829.0819) and add it to both sides.

Add '290829.0819' to each side of the equation.
-1078.571429x + 290829.0819 + x2 = -224495 + 290829.0819

Reorder the terms:
290829.0819 + -1078.571429x + x2 = -224495 + 290829.0819

Combine like terms: -224495 + 290829.0819 = 66334.0819
290829.0819 + -1078.571429x + x2 = 66334.0819

Factor a perfect square on the left side:
(x + -539.2857145)(x + -539.2857145) = 66334.0819

Calculate the square root of the right side: 257.554036854

Break this problem into two subproblems by setting 
(x + -539.2857145) equal to 257.554036854 and -257.554036854.

Subproblem 1

x + -539.2857145 = 257.554036854 Simplifying x + -539.2857145 = 257.554036854 Reorder the terms: -539.2857145 + x = 257.554036854 Solving -539.2857145 + x = 257.554036854 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '539.2857145' to each side of the equation. -539.2857145 + 539.2857145 + x = 257.554036854 + 539.2857145 Combine like terms: -539.2857145 + 539.2857145 = 0.0000000 0.0000000 + x = 257.554036854 + 539.2857145 x = 257.554036854 + 539.2857145 Combine like terms: 257.554036854 + 539.2857145 = 796.839751354 x = 796.839751354 Simplifying x = 796.839751354

Subproblem 2

x + -539.2857145 = -257.554036854 Simplifying x + -539.2857145 = -257.554036854 Reorder the terms: -539.2857145 + x = -257.554036854 Solving -539.2857145 + x = -257.554036854 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '539.2857145' to each side of the equation. -539.2857145 + 539.2857145 + x = -257.554036854 + 539.2857145 Combine like terms: -539.2857145 + 539.2857145 = 0.0000000 0.0000000 + x = -257.554036854 + 539.2857145 x = -257.554036854 + 539.2857145 Combine like terms: -257.554036854 + 539.2857145 = 281.731677646 x = 281.731677646 Simplifying x = 281.731677646

Solution

The solution to the problem is based on the solutions from the subproblems. x = {796.839751354, 281.731677646}

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