-36x^2+720x-48=0

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Solution for -36x^2+720x-48=0 equation: 


Simplifying
-36x2 + 720x + -48 = 0

Reorder the terms:
-48 + 720x + -36x2 = 0

Solving
-48 + 720x + -36x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-4 + 60x + -3x2) = 0

Ignore the factor 12.

Subproblem 1
Set the factor '(-4 + 60x + -3x2)' equal to zero and attempt to solve:

Simplifying
-4 + 60x + -3x2 = 0

Solving
-4 + 60x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
1.333333333 + -20x + x2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + -20x + -1.333333333 + x2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + -20x + x2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + -20x + x2 = 0 + -1.333333333
-20x + x2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
-20x + x2 = -1.333333333

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = -1.333333333 + 100

Reorder the terms:
100 + -20x + x2 = -1.333333333 + 100

Combine like terms: -1.333333333 + 100 = 98.666666667
100 + -20x + x2 = 98.666666667

Factor a perfect square on the left side:
(x + -10)(x + -10) = 98.666666667

Calculate the square root of the right side: 9.933109617

Break this problem into two subproblems by setting 
(x + -10) equal to 9.933109617 and -9.933109617.


Subproblem 1
x + -10 = 9.933109617

Simplifying
x + -10 = 9.933109617

Reorder the terms:
-10 + x = 9.933109617

Solving
-10 + x = 9.933109617

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = 9.933109617 + 10

Combine like terms: -10 + 10 = 0
0 + x = 9.933109617 + 10
x = 9.933109617 + 10

Combine like terms: 9.933109617 + 10 = 19.933109617
x = 19.933109617

Simplifying
x = 19.933109617


Subproblem 2
x + -10 = -9.933109617

Simplifying
x + -10 = -9.933109617

Reorder the terms:
-10 + x = -9.933109617

Solving
-10 + x = -9.933109617

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = -9.933109617 + 10

Combine like terms: -10 + 10 = 0
0 + x = -9.933109617 + 10
x = -9.933109617 + 10

Combine like terms: -9.933109617 + 10 = 0.066890383
x = 0.066890383

Simplifying
x = 0.066890383


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.933109617, 0.066890383}
Solution
x = {19.933109617, 0.066890383}

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