x^2+84x-18+9000x-8999x-x+3x=0

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Solution for x^2+84x-18+9000x-8999x-x+3x=0 equation:


Simplifying
x2 + 84x + -18 + 9000x + -8999x + -1x + 3x = 0

Reorder the terms:
-18 + 84x + 9000x + -8999x + -1x + 3x + x2 = 0

Combine like terms: 84x + 9000x = 9084x
-18 + 9084x + -8999x + -1x + 3x + x2 = 0

Combine like terms: 9084x + -8999x = 85x
-18 + 85x + -1x + 3x + x2 = 0

Combine like terms: 85x + -1x = 84x
-18 + 84x + 3x + x2 = 0

Combine like terms: 84x + 3x = 87x
-18 + 87x + x2 = 0

Solving
-18 + 87x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + 87x + 18 + x2 = 0 + 18

Reorder the terms:
-18 + 18 + 87x + x2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 87x + x2 = 0 + 18
87x + x2 = 0 + 18

Combine like terms: 0 + 18 = 18
87x + x2 = 18

The x term is 87x.  Take half its coefficient (43.5).
Square it (1892.25) and add it to both sides.

Add '1892.25' to each side of the equation.
87x + 1892.25 + x2 = 18 + 1892.25

Reorder the terms:
1892.25 + 87x + x2 = 18 + 1892.25

Combine like terms: 18 + 1892.25 = 1910.25
1892.25 + 87x + x2 = 1910.25

Factor a perfect square on the left side:
(x + 43.5)(x + 43.5) = 1910.25

Calculate the square root of the right side: 43.706406853

Break this problem into two subproblems by setting 
(x + 43.5) equal to 43.706406853 and -43.706406853.

Subproblem 1

x + 43.5 = 43.706406853 Simplifying x + 43.5 = 43.706406853 Reorder the terms: 43.5 + x = 43.706406853 Solving 43.5 + x = 43.706406853 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-43.5' to each side of the equation. 43.5 + -43.5 + x = 43.706406853 + -43.5 Combine like terms: 43.5 + -43.5 = 0.0 0.0 + x = 43.706406853 + -43.5 x = 43.706406853 + -43.5 Combine like terms: 43.706406853 + -43.5 = 0.206406853 x = 0.206406853 Simplifying x = 0.206406853

Subproblem 2

x + 43.5 = -43.706406853 Simplifying x + 43.5 = -43.706406853 Reorder the terms: 43.5 + x = -43.706406853 Solving 43.5 + x = -43.706406853 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-43.5' to each side of the equation. 43.5 + -43.5 + x = -43.706406853 + -43.5 Combine like terms: 43.5 + -43.5 = 0.0 0.0 + x = -43.706406853 + -43.5 x = -43.706406853 + -43.5 Combine like terms: -43.706406853 + -43.5 = -87.206406853 x = -87.206406853 Simplifying x = -87.206406853

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.206406853, -87.206406853}

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