x^2-5.5x+2.5=29929

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Solution for x^2-5.5x+2.5=29929 equation: 


Simplifying
x2 + -5.5x + 2.5 = 29929

Reorder the terms:
2.5 + -5.5x + x2 = 29929

Solving
2.5 + -5.5x + x2 = 29929

Solving for variable 'x'.

Reorder the terms:
2.5 + -29929 + -5.5x + x2 = 29929 + -29929

Combine like terms: 2.5 + -29929 = -29926.5
-29926.5 + -5.5x + x2 = 29929 + -29929

Combine like terms: 29929 + -29929 = 0
-29926.5 + -5.5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '29926.5' to each side of the equation.
-29926.5 + -5.5x + 29926.5 + x2 = 0 + 29926.5

Reorder the terms:
-29926.5 + 29926.5 + -5.5x + x2 = 0 + 29926.5

Combine like terms: -29926.5 + 29926.5 = 0.0
0.0 + -5.5x + x2 = 0 + 29926.5
-5.5x + x2 = 0 + 29926.5

Combine like terms: 0 + 29926.5 = 29926.5
-5.5x + x2 = 29926.5

The x term is -5.5x.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5x + 7.5625 + x2 = 29926.5 + 7.5625

Reorder the terms:
7.5625 + -5.5x + x2 = 29926.5 + 7.5625

Combine like terms: 29926.5 + 7.5625 = 29934.0625
7.5625 + -5.5x + x2 = 29934.0625

Factor a perfect square on the left side:
(x + -2.75)(x + -2.75) = 29934.0625

Calculate the square root of the right side: 173.014630884

Break this problem into two subproblems by setting 
(x + -2.75) equal to 173.014630884 and -173.014630884.


Subproblem 1
x + -2.75 = 173.014630884

Simplifying
x + -2.75 = 173.014630884

Reorder the terms:
-2.75 + x = 173.014630884

Solving
-2.75 + x = 173.014630884

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = 173.014630884 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = 173.014630884 + 2.75
x = 173.014630884 + 2.75

Combine like terms: 173.014630884 + 2.75 = 175.764630884
x = 175.764630884

Simplifying
x = 175.764630884


Subproblem 2
x + -2.75 = -173.014630884

Simplifying
x + -2.75 = -173.014630884

Reorder the terms:
-2.75 + x = -173.014630884

Solving
-2.75 + x = -173.014630884

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = -173.014630884 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = -173.014630884 + 2.75
x = -173.014630884 + 2.75

Combine like terms: -173.014630884 + 2.75 = -170.264630884
x = -170.264630884

Simplifying
x = -170.264630884


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {175.764630884, -170.264630884}

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