24*(2+2x)-6*x^2=0

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Solution for 24*(2+2x)-6*x^2=0 equation: 


Simplifying
24(2 + 2x) + -6x2 = 0
(2 * 24 + 2x * 24) + -6x2 = 0
(48 + 48x) + -6x2 = 0

Solving
48 + 48x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(8 + 8x + -1x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(8 + 8x + -1x2)' equal to zero and attempt to solve:

Simplifying
8 + 8x + -1x2 = 0

Solving
8 + 8x + -1x2 = 0

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

Divide each side by '-1'.
-8 + -8x + x2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -8x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + -8x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -8x + x2 = 0 + 8
-8x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
-8x + x2 = 8

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 8 + 16

Reorder the terms:
16 + -8x + x2 = 8 + 16

Combine like terms: 8 + 16 = 24
16 + -8x + x2 = 24

Factor a perfect square on the left side:
(x + -4)(x + -4) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(x + -4) equal to 4.898979486 and -4.898979486.


Subproblem 1
x + -4 = 4.898979486

Simplifying
x + -4 = 4.898979486

Reorder the terms:
-4 + x = 4.898979486

Solving
-4 + x = 4.898979486

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 4.898979486 + 4

Combine like terms: -4 + 4 = 0
0 + x = 4.898979486 + 4
x = 4.898979486 + 4

Combine like terms: 4.898979486 + 4 = 8.898979486
x = 8.898979486

Simplifying
x = 8.898979486


Subproblem 2
x + -4 = -4.898979486

Simplifying
x + -4 = -4.898979486

Reorder the terms:
-4 + x = -4.898979486

Solving
-4 + x = -4.898979486

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -4.898979486 + 4

Combine like terms: -4 + 4 = 0
0 + x = -4.898979486 + 4
x = -4.898979486 + 4

Combine like terms: -4.898979486 + 4 = -0.898979486
x = -0.898979486

Simplifying
x = -0.898979486


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.898979486, -0.898979486}
Solution
x = {8.898979486, -0.898979486}

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