9x^2-13734x+39000=0

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Solution for 9x^2-13734x+39000=0 equation: 


Simplifying
9x2 + -13734x + 39000 = 0

Reorder the terms:
39000 + -13734x + 9x2 = 0

Solving
39000 + -13734x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(13000 + -4578x + 3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(13000 + -4578x + 3x2)' equal to zero and attempt to solve:

Simplifying
13000 + -4578x + 3x2 = 0

Solving
13000 + -4578x + 3x2 = 0

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

Divide each side by '3'.
4333.333333 + -1526x + x2 = 0

Move the constant term to the right:

Add '-4333.333333' to each side of the equation.
4333.333333 + -1526x + -4333.333333 + x2 = 0 + -4333.333333

Reorder the terms:
4333.333333 + -4333.333333 + -1526x + x2 = 0 + -4333.333333

Combine like terms: 4333.333333 + -4333.333333 = 0.000000
0.000000 + -1526x + x2 = 0 + -4333.333333
-1526x + x2 = 0 + -4333.333333

Combine like terms: 0 + -4333.333333 = -4333.333333
-1526x + x2 = -4333.333333

The x term is -1526x.  Take half its coefficient (-763).
Square it (582169) and add it to both sides.

Add '582169' to each side of the equation.
-1526x + 582169 + x2 = -4333.333333 + 582169

Reorder the terms:
582169 + -1526x + x2 = -4333.333333 + 582169

Combine like terms: -4333.333333 + 582169 = 577835.666667
582169 + -1526x + x2 = 577835.666667

Factor a perfect square on the left side:
(x + -763)(x + -763) = 577835.666667

Calculate the square root of the right side: 760.155028048

Break this problem into two subproblems by setting 
(x + -763) equal to 760.155028048 and -760.155028048.


Subproblem 1
x + -763 = 760.155028048

Simplifying
x + -763 = 760.155028048

Reorder the terms:
-763 + x = 760.155028048

Solving
-763 + x = 760.155028048

Solving for variable 'x'.

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

Add '763' to each side of the equation.
-763 + 763 + x = 760.155028048 + 763

Combine like terms: -763 + 763 = 0
0 + x = 760.155028048 + 763
x = 760.155028048 + 763

Combine like terms: 760.155028048 + 763 = 1523.155028048
x = 1523.155028048

Simplifying
x = 1523.155028048


Subproblem 2
x + -763 = -760.155028048

Simplifying
x + -763 = -760.155028048

Reorder the terms:
-763 + x = -760.155028048

Solving
-763 + x = -760.155028048

Solving for variable 'x'.

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

Add '763' to each side of the equation.
-763 + 763 + x = -760.155028048 + 763

Combine like terms: -763 + 763 = 0
0 + x = -760.155028048 + 763
x = -760.155028048 + 763

Combine like terms: -760.155028048 + 763 = 2.844971952
x = 2.844971952

Simplifying
x = 2.844971952


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1523.155028048, 2.844971952}
Solution
x = {1523.155028048, 2.844971952}

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