-.003x^2+.23x+60=0

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Solution for -.003x^2+.23x+60=0 equation: 


Simplifying
-0.003x2 + 0.23x + 60 = 0

Reorder the terms:
60 + 0.23x + -0.003x2 = 0

Solving
60 + 0.23x + -0.003x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.003 the coefficient of the squared term: 

Divide each side by '-0.003'.
-20000 + -76.66666667x + x2 = 0

Move the constant term to the right:

Add '20000' to each side of the equation.
-20000 + -76.66666667x + 20000 + x2 = 0 + 20000

Reorder the terms:
-20000 + 20000 + -76.66666667x + x2 = 0 + 20000

Combine like terms: -20000 + 20000 = 0
0 + -76.66666667x + x2 = 0 + 20000
-76.66666667x + x2 = 0 + 20000

Combine like terms: 0 + 20000 = 20000
-76.66666667x + x2 = 20000

The x term is -76.66666667x.  Take half its coefficient (-38.33333334).
Square it (1469.444445) and add it to both sides.

Add '1469.444445' to each side of the equation.
-76.66666667x + 1469.444445 + x2 = 20000 + 1469.444445

Reorder the terms:
1469.444445 + -76.66666667x + x2 = 20000 + 1469.444445

Combine like terms: 20000 + 1469.444445 = 21469.444445
1469.444445 + -76.66666667x + x2 = 21469.444445

Factor a perfect square on the left side:
(x + -38.33333334)(x + -38.33333334) = 21469.444445

Calculate the square root of the right side: 146.524552362

Break this problem into two subproblems by setting 
(x + -38.33333334) equal to 146.524552362 and -146.524552362.


Subproblem 1
x + -38.33333334 = 146.524552362

Simplifying
x + -38.33333334 = 146.524552362

Reorder the terms:
-38.33333334 + x = 146.524552362

Solving
-38.33333334 + x = 146.524552362

Solving for variable 'x'.

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

Add '38.33333334' to each side of the equation.
-38.33333334 + 38.33333334 + x = 146.524552362 + 38.33333334

Combine like terms: -38.33333334 + 38.33333334 = 0.00000000
0.00000000 + x = 146.524552362 + 38.33333334
x = 146.524552362 + 38.33333334

Combine like terms: 146.524552362 + 38.33333334 = 184.857885702
x = 184.857885702

Simplifying
x = 184.857885702


Subproblem 2
x + -38.33333334 = -146.524552362

Simplifying
x + -38.33333334 = -146.524552362

Reorder the terms:
-38.33333334 + x = -146.524552362

Solving
-38.33333334 + x = -146.524552362

Solving for variable 'x'.

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

Add '38.33333334' to each side of the equation.
-38.33333334 + 38.33333334 + x = -146.524552362 + 38.33333334

Combine like terms: -38.33333334 + 38.33333334 = 0.00000000
0.00000000 + x = -146.524552362 + 38.33333334
x = -146.524552362 + 38.33333334

Combine like terms: -146.524552362 + 38.33333334 = -108.191219022
x = -108.191219022

Simplifying
x = -108.191219022


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {184.857885702, -108.191219022}

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