6x^2-x-1000=0

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Solution for 6x^2-x-1000=0 equation:


Simplifying
6x2 + -1x + -1000 = 0

Reorder the terms:
-1000 + -1x + 6x2 = 0

Solving
-1000 + -1x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
-166.6666667 + -0.1666666667x + x2 = 0

Move the constant term to the right:

Add '166.6666667' to each side of the equation.
-166.6666667 + -0.1666666667x + 166.6666667 + x2 = 0 + 166.6666667

Reorder the terms:
-166.6666667 + 166.6666667 + -0.1666666667x + x2 = 0 + 166.6666667

Combine like terms: -166.6666667 + 166.6666667 = 0.0000000
0.0000000 + -0.1666666667x + x2 = 0 + 166.6666667
-0.1666666667x + x2 = 0 + 166.6666667

Combine like terms: 0 + 166.6666667 = 166.6666667
-0.1666666667x + x2 = 166.6666667

The x term is -0.1666666667x.  Take half its coefficient (-0.08333333335).
Square it (0.006944444447) and add it to both sides.

Add '0.006944444447' to each side of the equation.
-0.1666666667x + 0.006944444447 + x2 = 166.6666667 + 0.006944444447

Reorder the terms:
0.006944444447 + -0.1666666667x + x2 = 166.6666667 + 0.006944444447

Combine like terms: 166.6666667 + 0.006944444447 = 166.673611144447
0.006944444447 + -0.1666666667x + x2 = 166.673611144447

Factor a perfect square on the left side:
(x + -0.08333333335)(x + -0.08333333335) = 166.673611144447

Calculate the square root of the right side: 12.910213443

Break this problem into two subproblems by setting 
(x + -0.08333333335) equal to 12.910213443 and -12.910213443.

Subproblem 1

x + -0.08333333335 = 12.910213443 Simplifying x + -0.08333333335 = 12.910213443 Reorder the terms: -0.08333333335 + x = 12.910213443 Solving -0.08333333335 + x = 12.910213443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = 12.910213443 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = 12.910213443 + 0.08333333335 x = 12.910213443 + 0.08333333335 Combine like terms: 12.910213443 + 0.08333333335 = 12.99354677635 x = 12.99354677635 Simplifying x = 12.99354677635

Subproblem 2

x + -0.08333333335 = -12.910213443 Simplifying x + -0.08333333335 = -12.910213443 Reorder the terms: -0.08333333335 + x = -12.910213443 Solving -0.08333333335 + x = -12.910213443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = -12.910213443 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = -12.910213443 + 0.08333333335 x = -12.910213443 + 0.08333333335 Combine like terms: -12.910213443 + 0.08333333335 = -12.82688010965 x = -12.82688010965 Simplifying x = -12.82688010965

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.99354677635, -12.82688010965}

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