a^2-1000a+240001=0

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Solution for a^2-1000a+240001=0 equation:


Simplifying
a2 + -1000a + 240001 = 0

Reorder the terms:
240001 + -1000a + a2 = 0

Solving
240001 + -1000a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-240001' to each side of the equation.
240001 + -1000a + -240001 + a2 = 0 + -240001

Reorder the terms:
240001 + -240001 + -1000a + a2 = 0 + -240001

Combine like terms: 240001 + -240001 = 0
0 + -1000a + a2 = 0 + -240001
-1000a + a2 = 0 + -240001

Combine like terms: 0 + -240001 = -240001
-1000a + a2 = -240001

The a term is -1000a.  Take half its coefficient (-500).
Square it (250000) and add it to both sides.

Add '250000' to each side of the equation.
-1000a + 250000 + a2 = -240001 + 250000

Reorder the terms:
250000 + -1000a + a2 = -240001 + 250000

Combine like terms: -240001 + 250000 = 9999
250000 + -1000a + a2 = 9999

Factor a perfect square on the left side:
(a + -500)(a + -500) = 9999

Calculate the square root of the right side: 99.994999875

Break this problem into two subproblems by setting 
(a + -500) equal to 99.994999875 and -99.994999875.

Subproblem 1

a + -500 = 99.994999875 Simplifying a + -500 = 99.994999875 Reorder the terms: -500 + a = 99.994999875 Solving -500 + a = 99.994999875 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '500' to each side of the equation. -500 + 500 + a = 99.994999875 + 500 Combine like terms: -500 + 500 = 0 0 + a = 99.994999875 + 500 a = 99.994999875 + 500 Combine like terms: 99.994999875 + 500 = 599.994999875 a = 599.994999875 Simplifying a = 599.994999875

Subproblem 2

a + -500 = -99.994999875 Simplifying a + -500 = -99.994999875 Reorder the terms: -500 + a = -99.994999875 Solving -500 + a = -99.994999875 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '500' to each side of the equation. -500 + 500 + a = -99.994999875 + 500 Combine like terms: -500 + 500 = 0 0 + a = -99.994999875 + 500 a = -99.994999875 + 500 Combine like terms: -99.994999875 + 500 = 400.005000125 a = 400.005000125 Simplifying a = 400.005000125

Solution

The solution to the problem is based on the solutions from the subproblems. a = {599.994999875, 400.005000125}

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