x(x+5)=250000

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Solution for x(x+5)=250000 equation: 


Simplifying
x(x + 5) = 250000

Reorder the terms:
x(5 + x) = 250000
(5 * x + x * x) = 250000
(5x + x2) = 250000

Solving
5x + x2 = 250000

Solving for variable 'x'.

Reorder the terms:
-250000 + 5x + x2 = 250000 + -250000

Combine like terms: 250000 + -250000 = 0
-250000 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '250000' to each side of the equation.
-250000 + 5x + 250000 + x2 = 0 + 250000

Reorder the terms:
-250000 + 250000 + 5x + x2 = 0 + 250000

Combine like terms: -250000 + 250000 = 0
0 + 5x + x2 = 0 + 250000
5x + x2 = 0 + 250000

Combine like terms: 0 + 250000 = 250000
5x + x2 = 250000

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 250000 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 250000 + 6.25

Combine like terms: 250000 + 6.25 = 250006.25
6.25 + 5x + x2 = 250006.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 250006.25

Calculate the square root of the right side: 500.006249961

Break this problem into two subproblems by setting 
(x + 2.5) equal to 500.006249961 and -500.006249961.


Subproblem 1
x + 2.5 = 500.006249961

Simplifying
x + 2.5 = 500.006249961

Reorder the terms:
2.5 + x = 500.006249961

Solving
2.5 + x = 500.006249961

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 500.006249961 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 500.006249961 + -2.5
x = 500.006249961 + -2.5

Combine like terms: 500.006249961 + -2.5 = 497.506249961
x = 497.506249961

Simplifying
x = 497.506249961


Subproblem 2
x + 2.5 = -500.006249961

Simplifying
x + 2.5 = -500.006249961

Reorder the terms:
2.5 + x = -500.006249961

Solving
2.5 + x = -500.006249961

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -500.006249961 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -500.006249961 + -2.5
x = -500.006249961 + -2.5

Combine like terms: -500.006249961 + -2.5 = -502.506249961
x = -502.506249961

Simplifying
x = -502.506249961


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {497.506249961, -502.506249961}

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