57-.0003x^2-.1x=0

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Solution for 57-.0003x^2-.1x=0 equation: 


Simplifying
57 + -0.0003x2 + -0.1x = 0

Reorder the terms:
57 + -0.1x + -0.0003x2 = 0

Solving
57 + -0.1x + -0.0003x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.0003 the coefficient of the squared term: 

Divide each side by '-0.0003'.
-190000 + 333.3333333x + x2 = 0

Move the constant term to the right:

Add '190000' to each side of the equation.
-190000 + 333.3333333x + 190000 + x2 = 0 + 190000

Reorder the terms:
-190000 + 190000 + 333.3333333x + x2 = 0 + 190000

Combine like terms: -190000 + 190000 = 0
0 + 333.3333333x + x2 = 0 + 190000
333.3333333x + x2 = 0 + 190000

Combine like terms: 0 + 190000 = 190000
333.3333333x + x2 = 190000

The x term is 333.3333333x.  Take half its coefficient (166.6666667).
Square it (27777.77779) and add it to both sides.

Add '27777.77779' to each side of the equation.
333.3333333x + 27777.77779 + x2 = 190000 + 27777.77779

Reorder the terms:
27777.77779 + 333.3333333x + x2 = 190000 + 27777.77779

Combine like terms: 190000 + 27777.77779 = 217777.77779
27777.77779 + 333.3333333x + x2 = 217777.77779

Factor a perfect square on the left side:
(x + 166.6666667)(x + 166.6666667) = 217777.77779

Calculate the square root of the right side: 466.66666668

Break this problem into two subproblems by setting 
(x + 166.6666667) equal to 466.66666668 and -466.66666668.


Subproblem 1
x + 166.6666667 = 466.66666668

Simplifying
x + 166.6666667 = 466.66666668

Reorder the terms:
166.6666667 + x = 466.66666668

Solving
166.6666667 + x = 466.66666668

Solving for variable 'x'.

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

Add '-166.6666667' to each side of the equation.
166.6666667 + -166.6666667 + x = 466.66666668 + -166.6666667

Combine like terms: 166.6666667 + -166.6666667 = 0.0000000
0.0000000 + x = 466.66666668 + -166.6666667
x = 466.66666668 + -166.6666667

Combine like terms: 466.66666668 + -166.6666667 = 299.99999998
x = 299.99999998

Simplifying
x = 299.99999998


Subproblem 2
x + 166.6666667 = -466.66666668

Simplifying
x + 166.6666667 = -466.66666668

Reorder the terms:
166.6666667 + x = -466.66666668

Solving
166.6666667 + x = -466.66666668

Solving for variable 'x'.

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

Add '-166.6666667' to each side of the equation.
166.6666667 + -166.6666667 + x = -466.66666668 + -166.6666667

Combine like terms: 166.6666667 + -166.6666667 = 0.0000000
0.0000000 + x = -466.66666668 + -166.6666667
x = -466.66666668 + -166.6666667

Combine like terms: -466.66666668 + -166.6666667 = -633.33333338
x = -633.33333338

Simplifying
x = -633.33333338


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {299.99999998, -633.33333338}

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