89000=2840x^2+5525x+5504

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Solution for 89000=2840x^2+5525x+5504 equation:


Simplifying
89000 = 2840x2 + 5525x + 5504

Reorder the terms:
89000 = 5504 + 5525x + 2840x2

Solving
89000 = 5504 + 5525x + 2840x2

Solving for variable 'x'.

Combine like terms: 89000 + -5504 = 83496
83496 + -5525x + -2840x2 = 5504 + 5525x + 2840x2 + -5504 + -5525x + -2840x2

Reorder the terms:
83496 + -5525x + -2840x2 = 5504 + -5504 + 5525x + -5525x + 2840x2 + -2840x2

Combine like terms: 5504 + -5504 = 0
83496 + -5525x + -2840x2 = 0 + 5525x + -5525x + 2840x2 + -2840x2
83496 + -5525x + -2840x2 = 5525x + -5525x + 2840x2 + -2840x2

Combine like terms: 5525x + -5525x = 0
83496 + -5525x + -2840x2 = 0 + 2840x2 + -2840x2
83496 + -5525x + -2840x2 = 2840x2 + -2840x2

Combine like terms: 2840x2 + -2840x2 = 0
83496 + -5525x + -2840x2 = 0

Begin completing the square.  Divide all terms by
-2840 the coefficient of the squared term: 

Divide each side by '-2840'.
-29.4 + 1.945422535x + x2 = 0

Move the constant term to the right:

Add '29.4' to each side of the equation.
-29.4 + 1.945422535x + 29.4 + x2 = 0 + 29.4

Reorder the terms:
-29.4 + 29.4 + 1.945422535x + x2 = 0 + 29.4

Combine like terms: -29.4 + 29.4 = 0.0
0.0 + 1.945422535x + x2 = 0 + 29.4
1.945422535x + x2 = 0 + 29.4

Combine like terms: 0 + 29.4 = 29.4
1.945422535x + x2 = 29.4

The x term is 1.945422535x.  Take half its coefficient (0.9727112675).
Square it (0.9461672099) and add it to both sides.

Add '0.9461672099' to each side of the equation.
1.945422535x + 0.9461672099 + x2 = 29.4 + 0.9461672099

Reorder the terms:
0.9461672099 + 1.945422535x + x2 = 29.4 + 0.9461672099

Combine like terms: 29.4 + 0.9461672099 = 30.3461672099
0.9461672099 + 1.945422535x + x2 = 30.3461672099

Factor a perfect square on the left side:
(x + 0.9727112675)(x + 0.9727112675) = 30.3461672099

Calculate the square root of the right side: 5.508735536

Break this problem into two subproblems by setting 
(x + 0.9727112675) equal to 5.508735536 and -5.508735536.

Subproblem 1

x + 0.9727112675 = 5.508735536 Simplifying x + 0.9727112675 = 5.508735536 Reorder the terms: 0.9727112675 + x = 5.508735536 Solving 0.9727112675 + x = 5.508735536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9727112675' to each side of the equation. 0.9727112675 + -0.9727112675 + x = 5.508735536 + -0.9727112675 Combine like terms: 0.9727112675 + -0.9727112675 = 0.0000000000 0.0000000000 + x = 5.508735536 + -0.9727112675 x = 5.508735536 + -0.9727112675 Combine like terms: 5.508735536 + -0.9727112675 = 4.5360242685 x = 4.5360242685 Simplifying x = 4.5360242685

Subproblem 2

x + 0.9727112675 = -5.508735536 Simplifying x + 0.9727112675 = -5.508735536 Reorder the terms: 0.9727112675 + x = -5.508735536 Solving 0.9727112675 + x = -5.508735536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9727112675' to each side of the equation. 0.9727112675 + -0.9727112675 + x = -5.508735536 + -0.9727112675 Combine like terms: 0.9727112675 + -0.9727112675 = 0.0000000000 0.0000000000 + x = -5.508735536 + -0.9727112675 x = -5.508735536 + -0.9727112675 Combine like terms: -5.508735536 + -0.9727112675 = -6.4814468035 x = -6.4814468035 Simplifying x = -6.4814468035

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.5360242685, -6.4814468035}

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