x^2+x-12000=0

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Solution for x^2+x-12000=0 equation:


Simplifying
x2 + x + -12000 = 0

Reorder the terms:
-12000 + x + x2 = 0

Solving
-12000 + x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '12000' to each side of the equation.
-12000 + x + 12000 + x2 = 0 + 12000

Reorder the terms:
-12000 + 12000 + x + x2 = 0 + 12000

Combine like terms: -12000 + 12000 = 0
0 + x + x2 = 0 + 12000
x + x2 = 0 + 12000

Combine like terms: 0 + 12000 = 12000
x + x2 = 12000

The x term is x.  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.
x + 0.25 + x2 = 12000 + 0.25

Reorder the terms:
0.25 + x + x2 = 12000 + 0.25

Combine like terms: 12000 + 0.25 = 12000.25
0.25 + x + x2 = 12000.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 12000.25

Calculate the square root of the right side: 109.545652584

Break this problem into two subproblems by setting 
(x + 0.5) equal to 109.545652584 and -109.545652584.

Subproblem 1

x + 0.5 = 109.545652584 Simplifying x + 0.5 = 109.545652584 Reorder the terms: 0.5 + x = 109.545652584 Solving 0.5 + x = 109.545652584 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 = 109.545652584 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 109.545652584 + -0.5 x = 109.545652584 + -0.5 Combine like terms: 109.545652584 + -0.5 = 109.045652584 x = 109.045652584 Simplifying x = 109.045652584

Subproblem 2

x + 0.5 = -109.545652584 Simplifying x + 0.5 = -109.545652584 Reorder the terms: 0.5 + x = -109.545652584 Solving 0.5 + x = -109.545652584 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 = -109.545652584 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -109.545652584 + -0.5 x = -109.545652584 + -0.5 Combine like terms: -109.545652584 + -0.5 = -110.045652584 x = -110.045652584 Simplifying x = -110.045652584

Solution

The solution to the problem is based on the solutions from the subproblems. x = {109.045652584, -110.045652584}

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