5.2x+(500000-x)7.7x=34000

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Solution for 5.2x+(500000-x)7.7x=34000 equation:


Simplifying
5.2x + (500000 + -1x) * 7.7x = 34000

Reorder the terms for easier multiplication:
5.2x + 7.7x(500000 + -1x) = 34000
5.2x + (500000 * 7.7x + -1x * 7.7x) = 34000
5.2x + (3850000x + -7.7x2) = 34000

Combine like terms: 5.2x + 3850000x = 3850005.2x
3850005.2x + -7.7x2 = 34000

Solving
3850005.2x + -7.7x2 = 34000

Solving for variable 'x'.

Reorder the terms:
-34000 + 3850005.2x + -7.7x2 = 34000 + -34000

Combine like terms: 34000 + -34000 = 0
-34000 + 3850005.2x + -7.7x2 = 0

Begin completing the square.  Divide all terms by
-7.7 the coefficient of the squared term: 

Divide each side by '-7.7'.
4415.584416 + -500000.6753x + x2 = 0

Move the constant term to the right:

Add '-4415.584416' to each side of the equation.
4415.584416 + -500000.6753x + -4415.584416 + x2 = 0 + -4415.584416

Reorder the terms:
4415.584416 + -4415.584416 + -500000.6753x + x2 = 0 + -4415.584416

Combine like terms: 4415.584416 + -4415.584416 = 0.000000
0.000000 + -500000.6753x + x2 = 0 + -4415.584416
-500000.6753x + x2 = 0 + -4415.584416

Combine like terms: 0 + -4415.584416 = -4415.584416
-500000.6753x + x2 = -4415.584416

The x term is -500000.6753x.  Take half its coefficient (-250000.3377).
Square it (62500168850) and add it to both sides.

Add '62500168850' to each side of the equation.
-500000.6753x + 62500168850 + x2 = -4415.584416 + 62500168850

Reorder the terms:
62500168850 + -500000.6753x + x2 = -4415.584416 + 62500168850

Combine like terms: -4415.584416 + 62500168850 = 62500164434.415584
62500168850 + -500000.6753x + x2 = 62500164434.415584

Factor a perfect square on the left side:
(x + -250000.3377)(x + -250000.3377) = 62500164434.415584

Calculate the square root of the right side: 250000.328868615

Break this problem into two subproblems by setting 
(x + -250000.3377) equal to 250000.328868615 and -250000.328868615.

Subproblem 1

x + -250000.3377 = 250000.328868615 Simplifying x + -250000.3377 = 250000.328868615 Reorder the terms: -250000.3377 + x = 250000.328868615 Solving -250000.3377 + x = 250000.328868615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '250000.3377' to each side of the equation. -250000.3377 + 250000.3377 + x = 250000.328868615 + 250000.3377 Combine like terms: -250000.3377 + 250000.3377 = 0.0000 0.0000 + x = 250000.328868615 + 250000.3377 x = 250000.328868615 + 250000.3377 Combine like terms: 250000.328868615 + 250000.3377 = 500000.666568615 x = 500000.666568615 Simplifying x = 500000.666568615

Subproblem 2

x + -250000.3377 = -250000.328868615 Simplifying x + -250000.3377 = -250000.328868615 Reorder the terms: -250000.3377 + x = -250000.328868615 Solving -250000.3377 + x = -250000.328868615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '250000.3377' to each side of the equation. -250000.3377 + 250000.3377 + x = -250000.328868615 + 250000.3377 Combine like terms: -250000.3377 + 250000.3377 = 0.0000 0.0000 + x = -250000.328868615 + 250000.3377 x = -250000.328868615 + 250000.3377 Combine like terms: -250000.328868615 + 250000.3377 = 0.008831385 x = 0.008831385 Simplifying x = 0.008831385

Solution

The solution to the problem is based on the solutions from the subproblems. x = {500000.666568615, 0.008831385}

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