0.0003x^2+0.1x-88=0

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Solution for 0.0003x^2+0.1x-88=0 equation: 


Simplifying
0.0003x2 + 0.1x + -88 = 0

Reorder the terms:
-88 + 0.1x + 0.0003x2 = 0

Solving
-88 + 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'.
-293333.3333 + 333.3333333x + x2 = 0

Move the constant term to the right:

Add '293333.3333' to each side of the equation.
-293333.3333 + 333.3333333x + 293333.3333 + x2 = 0 + 293333.3333

Reorder the terms:
-293333.3333 + 293333.3333 + 333.3333333x + x2 = 0 + 293333.3333

Combine like terms: -293333.3333 + 293333.3333 = 0.0000
0.0000 + 333.3333333x + x2 = 0 + 293333.3333
333.3333333x + x2 = 0 + 293333.3333

Combine like terms: 0 + 293333.3333 = 293333.3333
333.3333333x + x2 = 293333.3333

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 = 293333.3333 + 27777.77779

Reorder the terms:
27777.77779 + 333.3333333x + x2 = 293333.3333 + 27777.77779

Combine like terms: 293333.3333 + 27777.77779 = 321111.11109
27777.77779 + 333.3333333x + x2 = 321111.11109

Factor a perfect square on the left side:
(x + 166.6666667)(x + 166.6666667) = 321111.11109

Calculate the square root of the right side: 566.666666648

Break this problem into two subproblems by setting 
(x + 166.6666667) equal to 566.666666648 and -566.666666648.


Subproblem 1
x + 166.6666667 = 566.666666648

Simplifying
x + 166.6666667 = 566.666666648

Reorder the terms:
166.6666667 + x = 566.666666648

Solving
166.6666667 + x = 566.666666648

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 = 566.666666648 + -166.6666667

Combine like terms: 166.6666667 + -166.6666667 = 0.0000000
0.0000000 + x = 566.666666648 + -166.6666667
x = 566.666666648 + -166.6666667

Combine like terms: 566.666666648 + -166.6666667 = 399.999999948
x = 399.999999948

Simplifying
x = 399.999999948


Subproblem 2
x + 166.6666667 = -566.666666648

Simplifying
x + 166.6666667 = -566.666666648

Reorder the terms:
166.6666667 + x = -566.666666648

Solving
166.6666667 + x = -566.666666648

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 = -566.666666648 + -166.6666667

Combine like terms: 166.6666667 + -166.6666667 = 0.0000000
0.0000000 + x = -566.666666648 + -166.6666667
x = -566.666666648 + -166.6666667

Combine like terms: -566.666666648 + -166.6666667 = -733.333333348
x = -733.333333348

Simplifying
x = -733.333333348


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {399.999999948, -733.333333348}

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