0=x^2-60000x+2500000

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Solution for 0=x^2-60000x+2500000 equation:


Simplifying
0 = x2 + -60000x + 2500000

Reorder the terms:
0 = 2500000 + -60000x + x2

Solving
0 = 2500000 + -60000x + x2

Solving for variable 'x'.

Combine like terms: 0 + -2500000 = -2500000
-2500000 + 60000x + -1x2 = 2500000 + -60000x + x2 + -2500000 + 60000x + -1x2

Reorder the terms:
-2500000 + 60000x + -1x2 = 2500000 + -2500000 + -60000x + 60000x + x2 + -1x2

Combine like terms: 2500000 + -2500000 = 0
-2500000 + 60000x + -1x2 = 0 + -60000x + 60000x + x2 + -1x2
-2500000 + 60000x + -1x2 = -60000x + 60000x + x2 + -1x2

Combine like terms: -60000x + 60000x = 0
-2500000 + 60000x + -1x2 = 0 + x2 + -1x2
-2500000 + 60000x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-2500000 + 60000x + -1x2 = 0

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

Divide each side by '-1'.
2500000 + -60000x + x2 = 0

Move the constant term to the right:

Add '-2500000' to each side of the equation.
2500000 + -60000x + -2500000 + x2 = 0 + -2500000

Reorder the terms:
2500000 + -2500000 + -60000x + x2 = 0 + -2500000

Combine like terms: 2500000 + -2500000 = 0
0 + -60000x + x2 = 0 + -2500000
-60000x + x2 = 0 + -2500000

Combine like terms: 0 + -2500000 = -2500000
-60000x + x2 = -2500000

The x term is -60000x.  Take half its coefficient (-30000).
Square it (900000000) and add it to both sides.

Add '900000000' to each side of the equation.
-60000x + 900000000 + x2 = -2500000 + 900000000

Reorder the terms:
900000000 + -60000x + x2 = -2500000 + 900000000

Combine like terms: -2500000 + 900000000 = 897500000
900000000 + -60000x + x2 = 897500000

Factor a perfect square on the left side:
(x + -30000)(x + -30000) = 897500000

Calculate the square root of the right side: 29958.30435789

Break this problem into two subproblems by setting 
(x + -30000) equal to 29958.30435789 and -29958.30435789.

Subproblem 1

x + -30000 = 29958.30435789 Simplifying x + -30000 = 29958.30435789 Reorder the terms: -30000 + x = 29958.30435789 Solving -30000 + x = 29958.30435789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30000' to each side of the equation. -30000 + 30000 + x = 29958.30435789 + 30000 Combine like terms: -30000 + 30000 = 0 0 + x = 29958.30435789 + 30000 x = 29958.30435789 + 30000 Combine like terms: 29958.30435789 + 30000 = 59958.30435789 x = 59958.30435789 Simplifying x = 59958.30435789

Subproblem 2

x + -30000 = -29958.30435789 Simplifying x + -30000 = -29958.30435789 Reorder the terms: -30000 + x = -29958.30435789 Solving -30000 + x = -29958.30435789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30000' to each side of the equation. -30000 + 30000 + x = -29958.30435789 + 30000 Combine like terms: -30000 + 30000 = 0 0 + x = -29958.30435789 + 30000 x = -29958.30435789 + 30000 Combine like terms: -29958.30435789 + 30000 = 41.69564211 x = 41.69564211 Simplifying x = 41.69564211

Solution

The solution to the problem is based on the solutions from the subproblems. x = {59958.30435789, 41.69564211}

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