x^2-27000x+45000000=0

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Solution for x^2-27000x+45000000=0 equation:


Simplifying
x2 + -27000x + 45000000 = 0

Reorder the terms:
45000000 + -27000x + x2 = 0

Solving
45000000 + -27000x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-45000000' to each side of the equation.
45000000 + -27000x + -45000000 + x2 = 0 + -45000000

Reorder the terms:
45000000 + -45000000 + -27000x + x2 = 0 + -45000000

Combine like terms: 45000000 + -45000000 = 0
0 + -27000x + x2 = 0 + -45000000
-27000x + x2 = 0 + -45000000

Combine like terms: 0 + -45000000 = -45000000
-27000x + x2 = -45000000

The x term is -27000x.  Take half its coefficient (-13500).
Square it (182250000) and add it to both sides.

Add '182250000' to each side of the equation.
-27000x + 182250000 + x2 = -45000000 + 182250000

Reorder the terms:
182250000 + -27000x + x2 = -45000000 + 182250000

Combine like terms: -45000000 + 182250000 = 137250000
182250000 + -27000x + x2 = 137250000

Factor a perfect square on the left side:
(x + -13500)(x + -13500) = 137250000

Calculate the square root of the right side: 11715.37451386

Break this problem into two subproblems by setting 
(x + -13500) equal to 11715.37451386 and -11715.37451386.

Subproblem 1

x + -13500 = 11715.37451386 Simplifying x + -13500 = 11715.37451386 Reorder the terms: -13500 + x = 11715.37451386 Solving -13500 + x = 11715.37451386 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13500' to each side of the equation. -13500 + 13500 + x = 11715.37451386 + 13500 Combine like terms: -13500 + 13500 = 0 0 + x = 11715.37451386 + 13500 x = 11715.37451386 + 13500 Combine like terms: 11715.37451386 + 13500 = 25215.37451386 x = 25215.37451386 Simplifying x = 25215.37451386

Subproblem 2

x + -13500 = -11715.37451386 Simplifying x + -13500 = -11715.37451386 Reorder the terms: -13500 + x = -11715.37451386 Solving -13500 + x = -11715.37451386 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13500' to each side of the equation. -13500 + 13500 + x = -11715.37451386 + 13500 Combine like terms: -13500 + 13500 = 0 0 + x = -11715.37451386 + 13500 x = -11715.37451386 + 13500 Combine like terms: -11715.37451386 + 13500 = 1784.62548614 x = 1784.62548614 Simplifying x = 1784.62548614

Solution

The solution to the problem is based on the solutions from the subproblems. x = {25215.37451386, 1784.62548614}

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