(60-2x)x=60

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Solution for (60-2x)x=60 equation: 


Simplifying
(60 + -2x) * x = 60

Reorder the terms for easier multiplication:
x(60 + -2x) = 60
(60 * x + -2x * x) = 60
(60x + -2x2) = 60

Solving
60x + -2x2 = 60

Solving for variable 'x'.

Reorder the terms:
-60 + 60x + -2x2 = 60 + -60

Combine like terms: 60 + -60 = 0
-60 + 60x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-30 + 30x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-30 + 30x + -1x2)' equal to zero and attempt to solve:

Simplifying
-30 + 30x + -1x2 = 0

Solving
-30 + 30x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
30 + -30x + x2 = 0

Move the constant term to the right:

Add '-30' to each side of the equation.
30 + -30x + -30 + x2 = 0 + -30

Reorder the terms:
30 + -30 + -30x + x2 = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -30x + x2 = 0 + -30
-30x + x2 = 0 + -30

Combine like terms: 0 + -30 = -30
-30x + x2 = -30

The x term is -30x.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30x + 225 + x2 = -30 + 225

Reorder the terms:
225 + -30x + x2 = -30 + 225

Combine like terms: -30 + 225 = 195
225 + -30x + x2 = 195

Factor a perfect square on the left side:
(x + -15)(x + -15) = 195

Calculate the square root of the right side: 13.964240044

Break this problem into two subproblems by setting 
(x + -15) equal to 13.964240044 and -13.964240044.


Subproblem 1
x + -15 = 13.964240044

Simplifying
x + -15 = 13.964240044

Reorder the terms:
-15 + x = 13.964240044

Solving
-15 + x = 13.964240044

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x = 13.964240044 + 15

Combine like terms: -15 + 15 = 0
0 + x = 13.964240044 + 15
x = 13.964240044 + 15

Combine like terms: 13.964240044 + 15 = 28.964240044
x = 28.964240044

Simplifying
x = 28.964240044


Subproblem 2
x + -15 = -13.964240044

Simplifying
x + -15 = -13.964240044

Reorder the terms:
-15 + x = -13.964240044

Solving
-15 + x = -13.964240044

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x = -13.964240044 + 15

Combine like terms: -15 + 15 = 0
0 + x = -13.964240044 + 15
x = -13.964240044 + 15

Combine like terms: -13.964240044 + 15 = 1.035759956
x = 1.035759956

Simplifying
x = 1.035759956


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {28.964240044, 1.035759956}
Solution
x = {28.964240044, 1.035759956}

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