15000+5000x+20x^2=0

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Solution for 15000+5000x+20x^2=0 equation: 


Simplifying
15000 + 5000x + 20x2 = 0

Solving
15000 + 5000x + 20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '20'.
20(750 + 250x + x2) = 0

Ignore the factor 20.

Subproblem 1
Set the factor '(750 + 250x + x2)' equal to zero and attempt to solve:

Simplifying
750 + 250x + x2 = 0

Solving
750 + 250x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-750' to each side of the equation.
750 + 250x + -750 + x2 = 0 + -750

Reorder the terms:
750 + -750 + 250x + x2 = 0 + -750

Combine like terms: 750 + -750 = 0
0 + 250x + x2 = 0 + -750
250x + x2 = 0 + -750

Combine like terms: 0 + -750 = -750
250x + x2 = -750

The x term is 250x.  Take half its coefficient (125).
Square it (15625) and add it to both sides.

Add '15625' to each side of the equation.
250x + 15625 + x2 = -750 + 15625

Reorder the terms:
15625 + 250x + x2 = -750 + 15625

Combine like terms: -750 + 15625 = 14875
15625 + 250x + x2 = 14875

Factor a perfect square on the left side:
(x + 125)(x + 125) = 14875

Calculate the square root of the right side: 121.963109177

Break this problem into two subproblems by setting 
(x + 125) equal to 121.963109177 and -121.963109177.


Subproblem 1
x + 125 = 121.963109177

Simplifying
x + 125 = 121.963109177

Reorder the terms:
125 + x = 121.963109177

Solving
125 + x = 121.963109177

Solving for variable 'x'.

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

Add '-125' to each side of the equation.
125 + -125 + x = 121.963109177 + -125

Combine like terms: 125 + -125 = 0
0 + x = 121.963109177 + -125
x = 121.963109177 + -125

Combine like terms: 121.963109177 + -125 = -3.036890823
x = -3.036890823

Simplifying
x = -3.036890823


Subproblem 2
x + 125 = -121.963109177

Simplifying
x + 125 = -121.963109177

Reorder the terms:
125 + x = -121.963109177

Solving
125 + x = -121.963109177

Solving for variable 'x'.

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

Add '-125' to each side of the equation.
125 + -125 + x = -121.963109177 + -125

Combine like terms: 125 + -125 = 0
0 + x = -121.963109177 + -125
x = -121.963109177 + -125

Combine like terms: -121.963109177 + -125 = -246.963109177
x = -246.963109177

Simplifying
x = -246.963109177


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.036890823, -246.963109177}
Solution
x = {-3.036890823, -246.963109177}

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