4(x+6)x=4

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Solution for 4(x+6)x=4 equation: 


Simplifying
4(x + 6) * x = 4

Reorder the terms:
4(6 + x) * x = 4

Reorder the terms for easier multiplication:
4x(6 + x) = 4
(6 * 4x + x * 4x) = 4
(24x + 4x2) = 4

Solving
24x + 4x2 = 4

Solving for variable 'x'.

Reorder the terms:
-4 + 24x + 4x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + 24x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + 6x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-1 + 6x + x2)' equal to zero and attempt to solve:

Simplifying
-1 + 6x + x2 = 0

Solving
-1 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 6x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 6x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 6x + x2 = 0 + 1
6x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
6x + x2 = 1

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 1 + 9

Reorder the terms:
9 + 6x + x2 = 1 + 9

Combine like terms: 1 + 9 = 10
9 + 6x + x2 = 10

Factor a perfect square on the left side:
(x + 3)(x + 3) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(x + 3) equal to 3.16227766 and -3.16227766.


Subproblem 1
x + 3 = 3.16227766

Simplifying
x + 3 = 3.16227766

Reorder the terms:
3 + x = 3.16227766

Solving
3 + x = 3.16227766

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 3.16227766 + -3

Combine like terms: 3 + -3 = 0
0 + x = 3.16227766 + -3
x = 3.16227766 + -3

Combine like terms: 3.16227766 + -3 = 0.16227766
x = 0.16227766

Simplifying
x = 0.16227766


Subproblem 2
x + 3 = -3.16227766

Simplifying
x + 3 = -3.16227766

Reorder the terms:
3 + x = -3.16227766

Solving
3 + x = -3.16227766

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -3.16227766 + -3

Combine like terms: 3 + -3 = 0
0 + x = -3.16227766 + -3
x = -3.16227766 + -3

Combine like terms: -3.16227766 + -3 = -6.16227766
x = -6.16227766

Simplifying
x = -6.16227766


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.16227766, -6.16227766}
Solution
x = {0.16227766, -6.16227766}

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