3x^2+20x-3500=0

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Solution for 3x^2+20x-3500=0 equation:


Simplifying
3x2 + 20x + -3500 = 0

Reorder the terms:
-3500 + 20x + 3x2 = 0

Solving
-3500 + 20x + 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'.
-1166.666667 + 6.666666667x + x2 = 0

Move the constant term to the right:

Add '1166.666667' to each side of the equation.
-1166.666667 + 6.666666667x + 1166.666667 + x2 = 0 + 1166.666667

Reorder the terms:
-1166.666667 + 1166.666667 + 6.666666667x + x2 = 0 + 1166.666667

Combine like terms: -1166.666667 + 1166.666667 = 0.000000
0.000000 + 6.666666667x + x2 = 0 + 1166.666667
6.666666667x + x2 = 0 + 1166.666667

Combine like terms: 0 + 1166.666667 = 1166.666667
6.666666667x + x2 = 1166.666667

The x term is 6.666666667x.  Take half its coefficient (3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
6.666666667x + 11.11111112 + x2 = 1166.666667 + 11.11111112

Reorder the terms:
11.11111112 + 6.666666667x + x2 = 1166.666667 + 11.11111112

Combine like terms: 1166.666667 + 11.11111112 = 1177.77777812
11.11111112 + 6.666666667x + x2 = 1177.77777812

Factor a perfect square on the left side:
(x + 3.333333334)(x + 3.333333334) = 1177.77777812

Calculate the square root of the right side: 34.318767142

Break this problem into two subproblems by setting 
(x + 3.333333334) equal to 34.318767142 and -34.318767142.

Subproblem 1

x + 3.333333334 = 34.318767142 Simplifying x + 3.333333334 = 34.318767142 Reorder the terms: 3.333333334 + x = 34.318767142 Solving 3.333333334 + x = 34.318767142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.333333334' to each side of the equation. 3.333333334 + -3.333333334 + x = 34.318767142 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + x = 34.318767142 + -3.333333334 x = 34.318767142 + -3.333333334 Combine like terms: 34.318767142 + -3.333333334 = 30.985433808 x = 30.985433808 Simplifying x = 30.985433808

Subproblem 2

x + 3.333333334 = -34.318767142 Simplifying x + 3.333333334 = -34.318767142 Reorder the terms: 3.333333334 + x = -34.318767142 Solving 3.333333334 + x = -34.318767142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.333333334' to each side of the equation. 3.333333334 + -3.333333334 + x = -34.318767142 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + x = -34.318767142 + -3.333333334 x = -34.318767142 + -3.333333334 Combine like terms: -34.318767142 + -3.333333334 = -37.652100476 x = -37.652100476 Simplifying x = -37.652100476

Solution

The solution to the problem is based on the solutions from the subproblems. x = {30.985433808, -37.652100476}

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