3x^2-80x-350=0

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Solution for 3x^2-80x-350=0 equation:


Simplifying
3x2 + -80x + -350 = 0

Reorder the terms:
-350 + -80x + 3x2 = 0

Solving
-350 + -80x + 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'.
-116.6666667 + -26.66666667x + x2 = 0

Move the constant term to the right:

Add '116.6666667' to each side of the equation.
-116.6666667 + -26.66666667x + 116.6666667 + x2 = 0 + 116.6666667

Reorder the terms:
-116.6666667 + 116.6666667 + -26.66666667x + x2 = 0 + 116.6666667

Combine like terms: -116.6666667 + 116.6666667 = 0.0000000
0.0000000 + -26.66666667x + x2 = 0 + 116.6666667
-26.66666667x + x2 = 0 + 116.6666667

Combine like terms: 0 + 116.6666667 = 116.6666667
-26.66666667x + x2 = 116.6666667

The x term is -26.66666667x.  Take half its coefficient (-13.33333334).
Square it (177.7777780) and add it to both sides.

Add '177.7777780' to each side of the equation.
-26.66666667x + 177.7777780 + x2 = 116.6666667 + 177.7777780

Reorder the terms:
177.7777780 + -26.66666667x + x2 = 116.6666667 + 177.7777780

Combine like terms: 116.6666667 + 177.7777780 = 294.4444447
177.7777780 + -26.66666667x + x2 = 294.4444447

Factor a perfect square on the left side:
(x + -13.33333334)(x + -13.33333334) = 294.4444447

Calculate the square root of the right side: 17.159383576

Break this problem into two subproblems by setting 
(x + -13.33333334) equal to 17.159383576 and -17.159383576.

Subproblem 1

x + -13.33333334 = 17.159383576 Simplifying x + -13.33333334 = 17.159383576 Reorder the terms: -13.33333334 + x = 17.159383576 Solving -13.33333334 + x = 17.159383576 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.33333334' to each side of the equation. -13.33333334 + 13.33333334 + x = 17.159383576 + 13.33333334 Combine like terms: -13.33333334 + 13.33333334 = 0.00000000 0.00000000 + x = 17.159383576 + 13.33333334 x = 17.159383576 + 13.33333334 Combine like terms: 17.159383576 + 13.33333334 = 30.492716916 x = 30.492716916 Simplifying x = 30.492716916

Subproblem 2

x + -13.33333334 = -17.159383576 Simplifying x + -13.33333334 = -17.159383576 Reorder the terms: -13.33333334 + x = -17.159383576 Solving -13.33333334 + x = -17.159383576 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.33333334' to each side of the equation. -13.33333334 + 13.33333334 + x = -17.159383576 + 13.33333334 Combine like terms: -13.33333334 + 13.33333334 = 0.00000000 0.00000000 + x = -17.159383576 + 13.33333334 x = -17.159383576 + 13.33333334 Combine like terms: -17.159383576 + 13.33333334 = -3.826050236 x = -3.826050236 Simplifying x = -3.826050236

Solution

The solution to the problem is based on the solutions from the subproblems. x = {30.492716916, -3.826050236}

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