24=2x(12-x)

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Solution for 24=2x(12-x) equation: 


Simplifying
24 = 2x(12 + -1x)
24 = (12 * 2x + -1x * 2x)
24 = (24x + -2x2)

Solving
24 = 24x + -2x2

Solving for variable 'x'.

Reorder the terms:
24 + -24x + 2x2 = 24x + -24x + -2x2 + 2x2

Combine like terms: 24x + -24x = 0
24 + -24x + 2x2 = 0 + -2x2 + 2x2
24 + -24x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
24 + -24x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + -12x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(12 + -12x + x2)' equal to zero and attempt to solve:

Simplifying
12 + -12x + x2 = 0

Solving
12 + -12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + -12x + -12 + x2 = 0 + -12

Reorder the terms:
12 + -12 + -12x + x2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -12x + x2 = 0 + -12
-12x + x2 = 0 + -12

Combine like terms: 0 + -12 = -12
-12x + x2 = -12

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = -12 + 36

Reorder the terms:
36 + -12x + x2 = -12 + 36

Combine like terms: -12 + 36 = 24
36 + -12x + x2 = 24

Factor a perfect square on the left side:
(x + -6)(x + -6) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(x + -6) equal to 4.898979486 and -4.898979486.


Subproblem 1
x + -6 = 4.898979486

Simplifying
x + -6 = 4.898979486

Reorder the terms:
-6 + x = 4.898979486

Solving
-6 + x = 4.898979486

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = 4.898979486 + 6

Combine like terms: -6 + 6 = 0
0 + x = 4.898979486 + 6
x = 4.898979486 + 6

Combine like terms: 4.898979486 + 6 = 10.898979486
x = 10.898979486

Simplifying
x = 10.898979486


Subproblem 2
x + -6 = -4.898979486

Simplifying
x + -6 = -4.898979486

Reorder the terms:
-6 + x = -4.898979486

Solving
-6 + x = -4.898979486

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = -4.898979486 + 6

Combine like terms: -6 + 6 = 0
0 + x = -4.898979486 + 6
x = -4.898979486 + 6

Combine like terms: -4.898979486 + 6 = 1.101020514
x = 1.101020514

Simplifying
x = 1.101020514


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.898979486, 1.101020514}
Solution
x = {10.898979486, 1.101020514}

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