0.006x^2-0.22x+1.5=0

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Solution for 0.006x^2-0.22x+1.5=0 equation: 


Simplifying
0.006x2 + -0.22x + 1.5 = 0

Reorder the terms:
1.5 + -0.22x + 0.006x2 = 0

Solving
1.5 + -0.22x + 0.006x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.006'.
250 + -36.66666667x + x2 = 0

Move the constant term to the right:

Add '-250' to each side of the equation.
250 + -36.66666667x + -250 + x2 = 0 + -250

Reorder the terms:
250 + -250 + -36.66666667x + x2 = 0 + -250

Combine like terms: 250 + -250 = 0
0 + -36.66666667x + x2 = 0 + -250
-36.66666667x + x2 = 0 + -250

Combine like terms: 0 + -250 = -250
-36.66666667x + x2 = -250

The x term is -36.66666667x.  Take half its coefficient (-18.33333334).
Square it (336.1111114) and add it to both sides.

Add '336.1111114' to each side of the equation.
-36.66666667x + 336.1111114 + x2 = -250 + 336.1111114

Reorder the terms:
336.1111114 + -36.66666667x + x2 = -250 + 336.1111114

Combine like terms: -250 + 336.1111114 = 86.1111114
336.1111114 + -36.66666667x + x2 = 86.1111114

Factor a perfect square on the left side:
(x + -18.33333334)(x + -18.33333334) = 86.1111114

Calculate the square root of the right side: 9.279607287

Break this problem into two subproblems by setting 
(x + -18.33333334) equal to 9.279607287 and -9.279607287.


Subproblem 1
x + -18.33333334 = 9.279607287

Simplifying
x + -18.33333334 = 9.279607287

Reorder the terms:
-18.33333334 + x = 9.279607287

Solving
-18.33333334 + x = 9.279607287

Solving for variable 'x'.

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

Add '18.33333334' to each side of the equation.
-18.33333334 + 18.33333334 + x = 9.279607287 + 18.33333334

Combine like terms: -18.33333334 + 18.33333334 = 0.00000000
0.00000000 + x = 9.279607287 + 18.33333334
x = 9.279607287 + 18.33333334

Combine like terms: 9.279607287 + 18.33333334 = 27.612940627
x = 27.612940627

Simplifying
x = 27.612940627


Subproblem 2
x + -18.33333334 = -9.279607287

Simplifying
x + -18.33333334 = -9.279607287

Reorder the terms:
-18.33333334 + x = -9.279607287

Solving
-18.33333334 + x = -9.279607287

Solving for variable 'x'.

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

Add '18.33333334' to each side of the equation.
-18.33333334 + 18.33333334 + x = -9.279607287 + 18.33333334

Combine like terms: -18.33333334 + 18.33333334 = 0.00000000
0.00000000 + x = -9.279607287 + 18.33333334
x = -9.279607287 + 18.33333334

Combine like terms: -9.279607287 + 18.33333334 = 9.053726053
x = 9.053726053

Simplifying
x = 9.053726053


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {27.612940627, 9.053726053}

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