x^2-x-999=0

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Solution for x^2-x-999=0 equation:


Simplifying
x2 + -1x + -999 = 0

Reorder the terms:
-999 + -1x + x2 = 0

Solving
-999 + -1x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '999' to each side of the equation.
-999 + -1x + 999 + x2 = 0 + 999

Reorder the terms:
-999 + 999 + -1x + x2 = 0 + 999

Combine like terms: -999 + 999 = 0
0 + -1x + x2 = 0 + 999
-1x + x2 = 0 + 999

Combine like terms: 0 + 999 = 999
-1x + x2 = 999

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 999 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 999 + 0.25

Combine like terms: 999 + 0.25 = 999.25
0.25 + -1x + x2 = 999.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 999.25

Calculate the square root of the right side: 31.610915836

Break this problem into two subproblems by setting 
(x + -0.5) equal to 31.610915836 and -31.610915836.

Subproblem 1

x + -0.5 = 31.610915836 Simplifying x + -0.5 = 31.610915836 Reorder the terms: -0.5 + x = 31.610915836 Solving -0.5 + x = 31.610915836 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 31.610915836 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 31.610915836 + 0.5 x = 31.610915836 + 0.5 Combine like terms: 31.610915836 + 0.5 = 32.110915836 x = 32.110915836 Simplifying x = 32.110915836

Subproblem 2

x + -0.5 = -31.610915836 Simplifying x + -0.5 = -31.610915836 Reorder the terms: -0.5 + x = -31.610915836 Solving -0.5 + x = -31.610915836 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -31.610915836 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -31.610915836 + 0.5 x = -31.610915836 + 0.5 Combine like terms: -31.610915836 + 0.5 = -31.110915836 x = -31.110915836 Simplifying x = -31.110915836

Solution

The solution to the problem is based on the solutions from the subproblems. x = {32.110915836, -31.110915836}

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