x^2+11111x+1000=0

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Solution for x^2+11111x+1000=0 equation:


Simplifying
x2 + 11111x + 1000 = 0

Reorder the terms:
1000 + 11111x + x2 = 0

Solving
1000 + 11111x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-1000' to each side of the equation.
1000 + 11111x + -1000 + x2 = 0 + -1000

Reorder the terms:
1000 + -1000 + 11111x + x2 = 0 + -1000

Combine like terms: 1000 + -1000 = 0
0 + 11111x + x2 = 0 + -1000
11111x + x2 = 0 + -1000

Combine like terms: 0 + -1000 = -1000
11111x + x2 = -1000

The x term is 11111x.  Take half its coefficient (5555.5).
Square it (30863580.25) and add it to both sides.

Add '30863580.25' to each side of the equation.
11111x + 30863580.25 + x2 = -1000 + 30863580.25

Reorder the terms:
30863580.25 + 11111x + x2 = -1000 + 30863580.25

Combine like terms: -1000 + 30863580.25 = 30862580.25
30863580.25 + 11111x + x2 = 30862580.25

Factor a perfect square on the left side:
(x + 5555.5)(x + 5555.5) = 30862580.25

Calculate the square root of the right side: 5555.409998371

Break this problem into two subproblems by setting 
(x + 5555.5) equal to 5555.409998371 and -5555.409998371.

Subproblem 1

x + 5555.5 = 5555.409998371 Simplifying x + 5555.5 = 5555.409998371 Reorder the terms: 5555.5 + x = 5555.409998371 Solving 5555.5 + x = 5555.409998371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5555.5' to each side of the equation. 5555.5 + -5555.5 + x = 5555.409998371 + -5555.5 Combine like terms: 5555.5 + -5555.5 = 0.0 0.0 + x = 5555.409998371 + -5555.5 x = 5555.409998371 + -5555.5 Combine like terms: 5555.409998371 + -5555.5 = -0.090001629 x = -0.090001629 Simplifying x = -0.090001629

Subproblem 2

x + 5555.5 = -5555.409998371 Simplifying x + 5555.5 = -5555.409998371 Reorder the terms: 5555.5 + x = -5555.409998371 Solving 5555.5 + x = -5555.409998371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5555.5' to each side of the equation. 5555.5 + -5555.5 + x = -5555.409998371 + -5555.5 Combine like terms: 5555.5 + -5555.5 = 0.0 0.0 + x = -5555.409998371 + -5555.5 x = -5555.409998371 + -5555.5 Combine like terms: -5555.409998371 + -5555.5 = -11110.909998371 x = -11110.909998371 Simplifying x = -11110.909998371

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.090001629, -11110.909998371}

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