6x^2-240x+1728=0

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Solution for 6x^2-240x+1728=0 equation: 


Simplifying
6x2 + -240x + 1728 = 0

Reorder the terms:
1728 + -240x + 6x2 = 0

Solving
1728 + -240x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(288 + -40x + x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(288 + -40x + x2)' equal to zero and attempt to solve:

Simplifying
288 + -40x + x2 = 0

Solving
288 + -40x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-288' to each side of the equation.
288 + -40x + -288 + x2 = 0 + -288

Reorder the terms:
288 + -288 + -40x + x2 = 0 + -288

Combine like terms: 288 + -288 = 0
0 + -40x + x2 = 0 + -288
-40x + x2 = 0 + -288

Combine like terms: 0 + -288 = -288
-40x + x2 = -288

The x term is -40x.  Take half its coefficient (-20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
-40x + 400 + x2 = -288 + 400

Reorder the terms:
400 + -40x + x2 = -288 + 400

Combine like terms: -288 + 400 = 112
400 + -40x + x2 = 112

Factor a perfect square on the left side:
(x + -20)(x + -20) = 112

Calculate the square root of the right side: 10.583005244

Break this problem into two subproblems by setting 
(x + -20) equal to 10.583005244 and -10.583005244.


Subproblem 1
x + -20 = 10.583005244

Simplifying
x + -20 = 10.583005244

Reorder the terms:
-20 + x = 10.583005244

Solving
-20 + x = 10.583005244

Solving for variable 'x'.

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

Add '20' to each side of the equation.
-20 + 20 + x = 10.583005244 + 20

Combine like terms: -20 + 20 = 0
0 + x = 10.583005244 + 20
x = 10.583005244 + 20

Combine like terms: 10.583005244 + 20 = 30.583005244
x = 30.583005244

Simplifying
x = 30.583005244


Subproblem 2
x + -20 = -10.583005244

Simplifying
x + -20 = -10.583005244

Reorder the terms:
-20 + x = -10.583005244

Solving
-20 + x = -10.583005244

Solving for variable 'x'.

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

Add '20' to each side of the equation.
-20 + 20 + x = -10.583005244 + 20

Combine like terms: -20 + 20 = 0
0 + x = -10.583005244 + 20
x = -10.583005244 + 20

Combine like terms: -10.583005244 + 20 = 9.416994756
x = 9.416994756

Simplifying
x = 9.416994756


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {30.583005244, 9.416994756}
Solution
x = {30.583005244, 9.416994756}

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