4x^2-550x+5000=0

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Solution for 4x^2-550x+5000=0 equation: 


Simplifying
4x2 + -550x + 5000 = 0

Reorder the terms:
5000 + -550x + 4x2 = 0

Solving
5000 + -550x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(2500 + -275x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(2500 + -275x + 2x2)' equal to zero and attempt to solve:

Simplifying
2500 + -275x + 2x2 = 0

Solving
2500 + -275x + 2x2 = 0

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

Divide each side by '2'.
1250 + -137.5x + x2 = 0

Move the constant term to the right:

Add '-1250' to each side of the equation.
1250 + -137.5x + -1250 + x2 = 0 + -1250

Reorder the terms:
1250 + -1250 + -137.5x + x2 = 0 + -1250

Combine like terms: 1250 + -1250 = 0
0 + -137.5x + x2 = 0 + -1250
-137.5x + x2 = 0 + -1250

Combine like terms: 0 + -1250 = -1250
-137.5x + x2 = -1250

The x term is -137.5x.  Take half its coefficient (-68.75).
Square it (4726.5625) and add it to both sides.

Add '4726.5625' to each side of the equation.
-137.5x + 4726.5625 + x2 = -1250 + 4726.5625

Reorder the terms:
4726.5625 + -137.5x + x2 = -1250 + 4726.5625

Combine like terms: -1250 + 4726.5625 = 3476.5625
4726.5625 + -137.5x + x2 = 3476.5625

Factor a perfect square on the left side:
(x + -68.75)(x + -68.75) = 3476.5625

Calculate the square root of the right side: 58.962382075

Break this problem into two subproblems by setting 
(x + -68.75) equal to 58.962382075 and -58.962382075.


Subproblem 1
x + -68.75 = 58.962382075

Simplifying
x + -68.75 = 58.962382075

Reorder the terms:
-68.75 + x = 58.962382075

Solving
-68.75 + x = 58.962382075

Solving for variable 'x'.

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

Add '68.75' to each side of the equation.
-68.75 + 68.75 + x = 58.962382075 + 68.75

Combine like terms: -68.75 + 68.75 = 0.00
0.00 + x = 58.962382075 + 68.75
x = 58.962382075 + 68.75

Combine like terms: 58.962382075 + 68.75 = 127.712382075
x = 127.712382075

Simplifying
x = 127.712382075


Subproblem 2
x + -68.75 = -58.962382075

Simplifying
x + -68.75 = -58.962382075

Reorder the terms:
-68.75 + x = -58.962382075

Solving
-68.75 + x = -58.962382075

Solving for variable 'x'.

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

Add '68.75' to each side of the equation.
-68.75 + 68.75 + x = -58.962382075 + 68.75

Combine like terms: -68.75 + 68.75 = 0.00
0.00 + x = -58.962382075 + 68.75
x = -58.962382075 + 68.75

Combine like terms: -58.962382075 + 68.75 = 9.787617925
x = 9.787617925

Simplifying
x = 9.787617925


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {127.712382075, 9.787617925}
Solution
x = {127.712382075, 9.787617925}

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