3x^2+8x-2800=0

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Solution for 3x^2+8x-2800=0 equation:


Simplifying
3x2 + 8x + -2800 = 0

Reorder the terms:
-2800 + 8x + 3x2 = 0

Solving
-2800 + 8x + 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'.
-933.3333333 + 2.666666667x + x2 = 0

Move the constant term to the right:

Add '933.3333333' to each side of the equation.
-933.3333333 + 2.666666667x + 933.3333333 + x2 = 0 + 933.3333333

Reorder the terms:
-933.3333333 + 933.3333333 + 2.666666667x + x2 = 0 + 933.3333333

Combine like terms: -933.3333333 + 933.3333333 = 0.0000000
0.0000000 + 2.666666667x + x2 = 0 + 933.3333333
2.666666667x + x2 = 0 + 933.3333333

Combine like terms: 0 + 933.3333333 = 933.3333333
2.666666667x + x2 = 933.3333333

The x term is 2.666666667x.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667x + 1.777777780 + x2 = 933.3333333 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667x + x2 = 933.3333333 + 1.777777780

Combine like terms: 933.3333333 + 1.777777780 = 935.11111108
1.777777780 + 2.666666667x + x2 = 935.11111108

Factor a perfect square on the left side:
(x + 1.333333334)(x + 1.333333334) = 935.11111108

Calculate the square root of the right side: 30.579586509

Break this problem into two subproblems by setting 
(x + 1.333333334) equal to 30.579586509 and -30.579586509.

Subproblem 1

x + 1.333333334 = 30.579586509 Simplifying x + 1.333333334 = 30.579586509 Reorder the terms: 1.333333334 + x = 30.579586509 Solving 1.333333334 + x = 30.579586509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = 30.579586509 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 30.579586509 + -1.333333334 x = 30.579586509 + -1.333333334 Combine like terms: 30.579586509 + -1.333333334 = 29.246253175 x = 29.246253175 Simplifying x = 29.246253175

Subproblem 2

x + 1.333333334 = -30.579586509 Simplifying x + 1.333333334 = -30.579586509 Reorder the terms: 1.333333334 + x = -30.579586509 Solving 1.333333334 + x = -30.579586509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = -30.579586509 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -30.579586509 + -1.333333334 x = -30.579586509 + -1.333333334 Combine like terms: -30.579586509 + -1.333333334 = -31.912919843 x = -31.912919843 Simplifying x = -31.912919843

Solution

The solution to the problem is based on the solutions from the subproblems. x = {29.246253175, -31.912919843}

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