0.01x^2+x-600=0

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Solution for 0.01x^2+x-600=0 equation: 


Simplifying
0.01x2 + x + -600 = 0

Reorder the terms:
-600 + x + 0.01x2 = 0

Solving
-600 + x + 0.01x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.01'.
-60000 + 100x + x2 = 0

Move the constant term to the right:

Add '60000' to each side of the equation.
-60000 + 100x + 60000 + x2 = 0 + 60000

Reorder the terms:
-60000 + 60000 + 100x + x2 = 0 + 60000

Combine like terms: -60000 + 60000 = 0
0 + 100x + x2 = 0 + 60000
100x + x2 = 0 + 60000

Combine like terms: 0 + 60000 = 60000
100x + x2 = 60000

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
100x + 0.25 + x2 = 60000 + 0.25

Reorder the terms:
0.25 + 100x + x2 = 60000 + 0.25

Combine like terms: 60000 + 0.25 = 60000.25
0.25 + 100x + x2 = 60000.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 60000.25

Calculate the square root of the right side: 244.949484588

Break this problem into two subproblems by setting 
(x + 0.5) equal to 244.949484588 and -244.949484588.


Subproblem 1
x + 0.5 = 244.949484588

Simplifying
x + 0.5 = 244.949484588

Reorder the terms:
0.5 + x = 244.949484588

Solving
0.5 + x = 244.949484588

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 244.949484588 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 244.949484588 + -0.5
x = 244.949484588 + -0.5

Combine like terms: 244.949484588 + -0.5 = 244.449484588
x = 244.449484588

Simplifying
x = 244.449484588


Subproblem 2
x + 0.5 = -244.949484588

Simplifying
x + 0.5 = -244.949484588

Reorder the terms:
0.5 + x = -244.949484588

Solving
0.5 + x = -244.949484588

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -244.949484588 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -244.949484588 + -0.5
x = -244.949484588 + -0.5

Combine like terms: -244.949484588 + -0.5 = -245.449484588
x = -245.449484588

Simplifying
x = -245.449484588


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {244.449484588, -245.449484588}

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