0.6x^2-23x+60=0

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Solution for 0.6x^2-23x+60=0 equation: 


Simplifying
0.6x2 + -23x + 60 = 0

Reorder the terms:
60 + -23x + 0.6x2 = 0

Solving
60 + -23x + 0.6x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.6'.
100 + -38.33333333x + x2 = 0

Move the constant term to the right:

Add '-100' to each side of the equation.
100 + -38.33333333x + -100 + x2 = 0 + -100

Reorder the terms:
100 + -100 + -38.33333333x + x2 = 0 + -100

Combine like terms: 100 + -100 = 0
0 + -38.33333333x + x2 = 0 + -100
-38.33333333x + x2 = 0 + -100

Combine like terms: 0 + -100 = -100
-38.33333333x + x2 = -100

The x term is -38.33333333x.  Take half its coefficient (-19.16666667).
Square it (367.3611112) and add it to both sides.

Add '367.3611112' to each side of the equation.
-38.33333333x + 367.3611112 + x2 = -100 + 367.3611112

Reorder the terms:
367.3611112 + -38.33333333x + x2 = -100 + 367.3611112

Combine like terms: -100 + 367.3611112 = 267.3611112
367.3611112 + -38.33333333x + x2 = 267.3611112

Factor a perfect square on the left side:
(x + -19.16666667)(x + -19.16666667) = 267.3611112

Calculate the square root of the right side: 16.351180728

Break this problem into two subproblems by setting 
(x + -19.16666667) equal to 16.351180728 and -16.351180728.


Subproblem 1
x + -19.16666667 = 16.351180728

Simplifying
x + -19.16666667 = 16.351180728

Reorder the terms:
-19.16666667 + x = 16.351180728

Solving
-19.16666667 + x = 16.351180728

Solving for variable 'x'.

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

Add '19.16666667' to each side of the equation.
-19.16666667 + 19.16666667 + x = 16.351180728 + 19.16666667

Combine like terms: -19.16666667 + 19.16666667 = 0.00000000
0.00000000 + x = 16.351180728 + 19.16666667
x = 16.351180728 + 19.16666667

Combine like terms: 16.351180728 + 19.16666667 = 35.517847398
x = 35.517847398

Simplifying
x = 35.517847398


Subproblem 2
x + -19.16666667 = -16.351180728

Simplifying
x + -19.16666667 = -16.351180728

Reorder the terms:
-19.16666667 + x = -16.351180728

Solving
-19.16666667 + x = -16.351180728

Solving for variable 'x'.

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

Add '19.16666667' to each side of the equation.
-19.16666667 + 19.16666667 + x = -16.351180728 + 19.16666667

Combine like terms: -19.16666667 + 19.16666667 = 0.00000000
0.00000000 + x = -16.351180728 + 19.16666667
x = -16.351180728 + 19.16666667

Combine like terms: -16.351180728 + 19.16666667 = 2.815485942
x = 2.815485942

Simplifying
x = 2.815485942


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {35.517847398, 2.815485942}

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