4x^2+22x-53500=0

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Solution for 4x^2+22x-53500=0 equation: 


Simplifying
4x2 + 22x + -53500 = 0

Reorder the terms:
-53500 + 22x + 4x2 = 0

Solving
-53500 + 22x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-26750 + 11x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-26750 + 11x + 2x2)' equal to zero and attempt to solve:

Simplifying
-26750 + 11x + 2x2 = 0

Solving
-26750 + 11x + 2x2 = 0

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

Divide each side by '2'.
-13375 + 5.5x + x2 = 0

Move the constant term to the right:

Add '13375' to each side of the equation.
-13375 + 5.5x + 13375 + x2 = 0 + 13375

Reorder the terms:
-13375 + 13375 + 5.5x + x2 = 0 + 13375

Combine like terms: -13375 + 13375 = 0
0 + 5.5x + x2 = 0 + 13375
5.5x + x2 = 0 + 13375

Combine like terms: 0 + 13375 = 13375
5.5x + x2 = 13375

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 = 13375 + 7.5625

Reorder the terms:
7.5625 + 5.5x + x2 = 13375 + 7.5625

Combine like terms: 13375 + 7.5625 = 13382.5625
7.5625 + 5.5x + x2 = 13382.5625

Factor a perfect square on the left side:
(x + 2.75)(x + 2.75) = 13382.5625

Calculate the square root of the right side: 115.68302598

Break this problem into two subproblems by setting 
(x + 2.75) equal to 115.68302598 and -115.68302598.


Subproblem 1
x + 2.75 = 115.68302598

Simplifying
x + 2.75 = 115.68302598

Reorder the terms:
2.75 + x = 115.68302598

Solving
2.75 + x = 115.68302598

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 = 115.68302598 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + x = 115.68302598 + -2.75
x = 115.68302598 + -2.75

Combine like terms: 115.68302598 + -2.75 = 112.93302598
x = 112.93302598

Simplifying
x = 112.93302598


Subproblem 2
x + 2.75 = -115.68302598

Simplifying
x + 2.75 = -115.68302598

Reorder the terms:
2.75 + x = -115.68302598

Solving
2.75 + x = -115.68302598

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 = -115.68302598 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + x = -115.68302598 + -2.75
x = -115.68302598 + -2.75

Combine like terms: -115.68302598 + -2.75 = -118.43302598
x = -118.43302598

Simplifying
x = -118.43302598


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {112.93302598, -118.43302598}
Solution
x = {112.93302598, -118.43302598}

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