3x^2-800x-139850=0

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Solution for 3x^2-800x-139850=0 equation:


Simplifying
3x2 + -800x + -139850 = 0

Reorder the terms:
-139850 + -800x + 3x2 = 0

Solving
-139850 + -800x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-46616.66667 + -266.6666667x + x2 = 0

Move the constant term to the right:

Add '46616.66667' to each side of the equation.
-46616.66667 + -266.6666667x + 46616.66667 + x2 = 0 + 46616.66667

Reorder the terms:
-46616.66667 + 46616.66667 + -266.6666667x + x2 = 0 + 46616.66667

Combine like terms: -46616.66667 + 46616.66667 = 0.00000
0.00000 + -266.6666667x + x2 = 0 + 46616.66667
-266.6666667x + x2 = 0 + 46616.66667

Combine like terms: 0 + 46616.66667 = 46616.66667
-266.6666667x + x2 = 46616.66667

The x term is -266.6666667x.  Take half its coefficient (-133.3333334).
Square it (17777.77780) and add it to both sides.

Add '17777.77780' to each side of the equation.
-266.6666667x + 17777.77780 + x2 = 46616.66667 + 17777.77780

Reorder the terms:
17777.77780 + -266.6666667x + x2 = 46616.66667 + 17777.77780

Combine like terms: 46616.66667 + 17777.77780 = 64394.44447
17777.77780 + -266.6666667x + x2 = 64394.44447

Factor a perfect square on the left side:
(x + -133.3333334)(x + -133.3333334) = 64394.44447

Calculate the square root of the right side: 253.760604645

Break this problem into two subproblems by setting 
(x + -133.3333334) equal to 253.760604645 and -253.760604645.

Subproblem 1

x + -133.3333334 = 253.760604645 Simplifying x + -133.3333334 = 253.760604645 Reorder the terms: -133.3333334 + x = 253.760604645 Solving -133.3333334 + x = 253.760604645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '133.3333334' to each side of the equation. -133.3333334 + 133.3333334 + x = 253.760604645 + 133.3333334 Combine like terms: -133.3333334 + 133.3333334 = 0.0000000 0.0000000 + x = 253.760604645 + 133.3333334 x = 253.760604645 + 133.3333334 Combine like terms: 253.760604645 + 133.3333334 = 387.093938045 x = 387.093938045 Simplifying x = 387.093938045

Subproblem 2

x + -133.3333334 = -253.760604645 Simplifying x + -133.3333334 = -253.760604645 Reorder the terms: -133.3333334 + x = -253.760604645 Solving -133.3333334 + x = -253.760604645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '133.3333334' to each side of the equation. -133.3333334 + 133.3333334 + x = -253.760604645 + 133.3333334 Combine like terms: -133.3333334 + 133.3333334 = 0.0000000 0.0000000 + x = -253.760604645 + 133.3333334 x = -253.760604645 + 133.3333334 Combine like terms: -253.760604645 + 133.3333334 = -120.427271245 x = -120.427271245 Simplifying x = -120.427271245

Solution

The solution to the problem is based on the solutions from the subproblems. x = {387.093938045, -120.427271245}

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