5x^2-3600x+100000=0

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Solution for 5x^2-3600x+100000=0 equation: 


Simplifying
5x2 + -3600x + 100000 = 0

Reorder the terms:
100000 + -3600x + 5x2 = 0

Solving
100000 + -3600x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(20000 + -720x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(20000 + -720x + x2)' equal to zero and attempt to solve:

Simplifying
20000 + -720x + x2 = 0

Solving
20000 + -720x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-20000' to each side of the equation.
20000 + -720x + -20000 + x2 = 0 + -20000

Reorder the terms:
20000 + -20000 + -720x + x2 = 0 + -20000

Combine like terms: 20000 + -20000 = 0
0 + -720x + x2 = 0 + -20000
-720x + x2 = 0 + -20000

Combine like terms: 0 + -20000 = -20000
-720x + x2 = -20000

The x term is -720x.  Take half its coefficient (-360).
Square it (129600) and add it to both sides.

Add '129600' to each side of the equation.
-720x + 129600 + x2 = -20000 + 129600

Reorder the terms:
129600 + -720x + x2 = -20000 + 129600

Combine like terms: -20000 + 129600 = 109600
129600 + -720x + x2 = 109600

Factor a perfect square on the left side:
(x + -360)(x + -360) = 109600

Calculate the square root of the right side: 331.058907145

Break this problem into two subproblems by setting 
(x + -360) equal to 331.058907145 and -331.058907145.


Subproblem 1
x + -360 = 331.058907145

Simplifying
x + -360 = 331.058907145

Reorder the terms:
-360 + x = 331.058907145

Solving
-360 + x = 331.058907145

Solving for variable 'x'.

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

Add '360' to each side of the equation.
-360 + 360 + x = 331.058907145 + 360

Combine like terms: -360 + 360 = 0
0 + x = 331.058907145 + 360
x = 331.058907145 + 360

Combine like terms: 331.058907145 + 360 = 691.058907145
x = 691.058907145

Simplifying
x = 691.058907145


Subproblem 2
x + -360 = -331.058907145

Simplifying
x + -360 = -331.058907145

Reorder the terms:
-360 + x = -331.058907145

Solving
-360 + x = -331.058907145

Solving for variable 'x'.

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

Add '360' to each side of the equation.
-360 + 360 + x = -331.058907145 + 360

Combine like terms: -360 + 360 = 0
0 + x = -331.058907145 + 360
x = -331.058907145 + 360

Combine like terms: -331.058907145 + 360 = 28.941092855
x = 28.941092855

Simplifying
x = 28.941092855


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {691.058907145, 28.941092855}
Solution
x = {691.058907145, 28.941092855}

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