0.001x^2+1.2x+60=0

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Solution for 0.001x^2+1.2x+60=0 equation: 


Simplifying
0.001x2 + 1.2x + 60 = 0

Reorder the terms:
60 + 1.2x + 0.001x2 = 0

Solving
60 + 1.2x + 0.001x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.001'.
60000 + 1200x + x2 = 0

Move the constant term to the right:

Add '-60000' to each side of the equation.
60000 + 1200x + -60000 + x2 = 0 + -60000

Reorder the terms:
60000 + -60000 + 1200x + x2 = 0 + -60000

Combine like terms: 60000 + -60000 = 0
0 + 1200x + x2 = 0 + -60000
1200x + x2 = 0 + -60000

Combine like terms: 0 + -60000 = -60000
1200x + x2 = -60000

The x term is 1200x.  Take half its coefficient (600).
Square it (360000) and add it to both sides.

Add '360000' to each side of the equation.
1200x + 360000 + x2 = -60000 + 360000

Reorder the terms:
360000 + 1200x + x2 = -60000 + 360000

Combine like terms: -60000 + 360000 = 300000
360000 + 1200x + x2 = 300000

Factor a perfect square on the left side:
(x + 600)(x + 600) = 300000

Calculate the square root of the right side: 547.722557505

Break this problem into two subproblems by setting 
(x + 600) equal to 547.722557505 and -547.722557505.


Subproblem 1
x + 600 = 547.722557505

Simplifying
x + 600 = 547.722557505

Reorder the terms:
600 + x = 547.722557505

Solving
600 + x = 547.722557505

Solving for variable 'x'.

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

Add '-600' to each side of the equation.
600 + -600 + x = 547.722557505 + -600

Combine like terms: 600 + -600 = 0
0 + x = 547.722557505 + -600
x = 547.722557505 + -600

Combine like terms: 547.722557505 + -600 = -52.277442495
x = -52.277442495

Simplifying
x = -52.277442495


Subproblem 2
x + 600 = -547.722557505

Simplifying
x + 600 = -547.722557505

Reorder the terms:
600 + x = -547.722557505

Solving
600 + x = -547.722557505

Solving for variable 'x'.

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

Add '-600' to each side of the equation.
600 + -600 + x = -547.722557505 + -600

Combine like terms: 600 + -600 = 0
0 + x = -547.722557505 + -600
x = -547.722557505 + -600

Combine like terms: -547.722557505 + -600 = -1147.722557505
x = -1147.722557505

Simplifying
x = -1147.722557505


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-52.277442495, -1147.722557505}

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