4x^2-50x-1000=0

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Solution for 4x^2-50x-1000=0 equation: 


Simplifying
4x2 + -50x + -1000 = 0

Reorder the terms:
-1000 + -50x + 4x2 = 0

Solving
-1000 + -50x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-500 + -25x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-500 + -25x + 2x2)' equal to zero and attempt to solve:

Simplifying
-500 + -25x + 2x2 = 0

Solving
-500 + -25x + 2x2 = 0

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

Divide each side by '2'.
-250 + -12.5x + x2 = 0

Move the constant term to the right:

Add '250' to each side of the equation.
-250 + -12.5x + 250 + x2 = 0 + 250

Reorder the terms:
-250 + 250 + -12.5x + x2 = 0 + 250

Combine like terms: -250 + 250 = 0
0 + -12.5x + x2 = 0 + 250
-12.5x + x2 = 0 + 250

Combine like terms: 0 + 250 = 250
-12.5x + x2 = 250

The x term is -12.5x.  Take half its coefficient (-6.25).
Square it (39.0625) and add it to both sides.

Add '39.0625' to each side of the equation.
-12.5x + 39.0625 + x2 = 250 + 39.0625

Reorder the terms:
39.0625 + -12.5x + x2 = 250 + 39.0625

Combine like terms: 250 + 39.0625 = 289.0625
39.0625 + -12.5x + x2 = 289.0625

Factor a perfect square on the left side:
(x + -6.25)(x + -6.25) = 289.0625

Calculate the square root of the right side: 17.001838136

Break this problem into two subproblems by setting 
(x + -6.25) equal to 17.001838136 and -17.001838136.


Subproblem 1
x + -6.25 = 17.001838136

Simplifying
x + -6.25 = 17.001838136

Reorder the terms:
-6.25 + x = 17.001838136

Solving
-6.25 + x = 17.001838136

Solving for variable 'x'.

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

Add '6.25' to each side of the equation.
-6.25 + 6.25 + x = 17.001838136 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + x = 17.001838136 + 6.25
x = 17.001838136 + 6.25

Combine like terms: 17.001838136 + 6.25 = 23.251838136
x = 23.251838136

Simplifying
x = 23.251838136


Subproblem 2
x + -6.25 = -17.001838136

Simplifying
x + -6.25 = -17.001838136

Reorder the terms:
-6.25 + x = -17.001838136

Solving
-6.25 + x = -17.001838136

Solving for variable 'x'.

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

Add '6.25' to each side of the equation.
-6.25 + 6.25 + x = -17.001838136 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + x = -17.001838136 + 6.25
x = -17.001838136 + 6.25

Combine like terms: -17.001838136 + 6.25 = -10.751838136
x = -10.751838136

Simplifying
x = -10.751838136


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {23.251838136, -10.751838136}
Solution
x = {23.251838136, -10.751838136}

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