175000=x(x+3)

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Solution for 175000=x(x+3) equation: 


Simplifying
175000 = x(x + 3)

Reorder the terms:
175000 = x(3 + x)
175000 = (3 * x + x * x)
175000 = (3x + x2)

Solving
175000 = 3x + x2

Solving for variable 'x'.

Reorder the terms:
175000 + -3x + -1x2 = 3x + -3x + x2 + -1x2

Combine like terms: 3x + -3x = 0
175000 + -3x + -1x2 = 0 + x2 + -1x2
175000 + -3x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
175000 + -3x + -1x2 = 0

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

Divide each side by '-1'.
-175000 + 3x + x2 = 0

Move the constant term to the right:

Add '175000' to each side of the equation.
-175000 + 3x + 175000 + x2 = 0 + 175000

Reorder the terms:
-175000 + 175000 + 3x + x2 = 0 + 175000

Combine like terms: -175000 + 175000 = 0
0 + 3x + x2 = 0 + 175000
3x + x2 = 0 + 175000

Combine like terms: 0 + 175000 = 175000
3x + x2 = 175000

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 175000 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 175000 + 2.25

Combine like terms: 175000 + 2.25 = 175002.25
2.25 + 3x + x2 = 175002.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 175002.25

Calculate the square root of the right side: 418.332702523

Break this problem into two subproblems by setting 
(x + 1.5) equal to 418.332702523 and -418.332702523.


Subproblem 1
x + 1.5 = 418.332702523

Simplifying
x + 1.5 = 418.332702523

Reorder the terms:
1.5 + x = 418.332702523

Solving
1.5 + x = 418.332702523

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 418.332702523 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 418.332702523 + -1.5
x = 418.332702523 + -1.5

Combine like terms: 418.332702523 + -1.5 = 416.832702523
x = 416.832702523

Simplifying
x = 416.832702523


Subproblem 2
x + 1.5 = -418.332702523

Simplifying
x + 1.5 = -418.332702523

Reorder the terms:
1.5 + x = -418.332702523

Solving
1.5 + x = -418.332702523

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -418.332702523 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -418.332702523 + -1.5
x = -418.332702523 + -1.5

Combine like terms: -418.332702523 + -1.5 = -419.832702523
x = -419.832702523

Simplifying
x = -419.832702523


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {416.832702523, -419.832702523}

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