6(x^2-24x+144)=1000

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Solution for 6(x^2-24x+144)=1000 equation: 


Simplifying
6(x2 + -24x + 144) = 1000

Reorder the terms:
6(144 + -24x + x2) = 1000
(144 * 6 + -24x * 6 + x2 * 6) = 1000
(864 + -144x + 6x2) = 1000

Solving
864 + -144x + 6x2 = 1000

Solving for variable 'x'.

Reorder the terms:
864 + -1000 + -144x + 6x2 = 1000 + -1000

Combine like terms: 864 + -1000 = -136
-136 + -144x + 6x2 = 1000 + -1000

Combine like terms: 1000 + -1000 = 0
-136 + -144x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-68 + -72x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-68 + -72x + 3x2)' equal to zero and attempt to solve:

Simplifying
-68 + -72x + 3x2 = 0

Solving
-68 + -72x + 3x2 = 0

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

Divide each side by '3'.
-22.66666667 + -24x + x2 = 0

Move the constant term to the right:

Add '22.66666667' to each side of the equation.
-22.66666667 + -24x + 22.66666667 + x2 = 0 + 22.66666667

Reorder the terms:
-22.66666667 + 22.66666667 + -24x + x2 = 0 + 22.66666667

Combine like terms: -22.66666667 + 22.66666667 = 0.00000000
0.00000000 + -24x + x2 = 0 + 22.66666667
-24x + x2 = 0 + 22.66666667

Combine like terms: 0 + 22.66666667 = 22.66666667
-24x + x2 = 22.66666667

The x term is -24x.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24x + 144 + x2 = 22.66666667 + 144

Reorder the terms:
144 + -24x + x2 = 22.66666667 + 144

Combine like terms: 22.66666667 + 144 = 166.66666667
144 + -24x + x2 = 166.66666667

Factor a perfect square on the left side:
(x + -12)(x + -12) = 166.66666667

Calculate the square root of the right side: 12.909944487

Break this problem into two subproblems by setting 
(x + -12) equal to 12.909944487 and -12.909944487.


Subproblem 1
x + -12 = 12.909944487

Simplifying
x + -12 = 12.909944487

Reorder the terms:
-12 + x = 12.909944487

Solving
-12 + x = 12.909944487

Solving for variable 'x'.

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

Add '12' to each side of the equation.
-12 + 12 + x = 12.909944487 + 12

Combine like terms: -12 + 12 = 0
0 + x = 12.909944487 + 12
x = 12.909944487 + 12

Combine like terms: 12.909944487 + 12 = 24.909944487
x = 24.909944487

Simplifying
x = 24.909944487


Subproblem 2
x + -12 = -12.909944487

Simplifying
x + -12 = -12.909944487

Reorder the terms:
-12 + x = -12.909944487

Solving
-12 + x = -12.909944487

Solving for variable 'x'.

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

Add '12' to each side of the equation.
-12 + 12 + x = -12.909944487 + 12

Combine like terms: -12 + 12 = 0
0 + x = -12.909944487 + 12
x = -12.909944487 + 12

Combine like terms: -12.909944487 + 12 = -0.909944487
x = -0.909944487

Simplifying
x = -0.909944487


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {24.909944487, -0.909944487}
Solution
x = {24.909944487, -0.909944487}

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