-16x^2+10000x+1440000=0

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Solution for -16x^2+10000x+1440000=0 equation: 


Simplifying
-16x2 + 10000x + 1440000 = 0

Reorder the terms:
1440000 + 10000x + -16x2 = 0

Solving
1440000 + 10000x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '16'.
16(90000 + 625x + -1x2) = 0

Ignore the factor 16.

Subproblem 1
Set the factor '(90000 + 625x + -1x2)' equal to zero and attempt to solve:

Simplifying
90000 + 625x + -1x2 = 0

Solving
90000 + 625x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-90000 + -625x + x2 = 0

Move the constant term to the right:

Add '90000' to each side of the equation.
-90000 + -625x + 90000 + x2 = 0 + 90000

Reorder the terms:
-90000 + 90000 + -625x + x2 = 0 + 90000

Combine like terms: -90000 + 90000 = 0
0 + -625x + x2 = 0 + 90000
-625x + x2 = 0 + 90000

Combine like terms: 0 + 90000 = 90000
-625x + x2 = 90000

The x term is -625x.  Take half its coefficient (-312.5).
Square it (97656.25) and add it to both sides.

Add '97656.25' to each side of the equation.
-625x + 97656.25 + x2 = 90000 + 97656.25

Reorder the terms:
97656.25 + -625x + x2 = 90000 + 97656.25

Combine like terms: 90000 + 97656.25 = 187656.25
97656.25 + -625x + x2 = 187656.25

Factor a perfect square on the left side:
(x + -312.5)(x + -312.5) = 187656.25

Calculate the square root of the right side: 433.193086279

Break this problem into two subproblems by setting 
(x + -312.5) equal to 433.193086279 and -433.193086279.


Subproblem 1
x + -312.5 = 433.193086279

Simplifying
x + -312.5 = 433.193086279

Reorder the terms:
-312.5 + x = 433.193086279

Solving
-312.5 + x = 433.193086279

Solving for variable 'x'.

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

Add '312.5' to each side of the equation.
-312.5 + 312.5 + x = 433.193086279 + 312.5

Combine like terms: -312.5 + 312.5 = 0.0
0.0 + x = 433.193086279 + 312.5
x = 433.193086279 + 312.5

Combine like terms: 433.193086279 + 312.5 = 745.693086279
x = 745.693086279

Simplifying
x = 745.693086279


Subproblem 2
x + -312.5 = -433.193086279

Simplifying
x + -312.5 = -433.193086279

Reorder the terms:
-312.5 + x = -433.193086279

Solving
-312.5 + x = -433.193086279

Solving for variable 'x'.

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

Add '312.5' to each side of the equation.
-312.5 + 312.5 + x = -433.193086279 + 312.5

Combine like terms: -312.5 + 312.5 = 0.0
0.0 + x = -433.193086279 + 312.5
x = -433.193086279 + 312.5

Combine like terms: -433.193086279 + 312.5 = -120.693086279
x = -120.693086279

Simplifying
x = -120.693086279


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {745.693086279, -120.693086279}
Solution
x = {745.693086279, -120.693086279}

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