3(x-4)(x-4)=15

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Solution for 3(x-4)(x-4)=15 equation: 


Simplifying
3(x + -4)(x + -4) = 15

Reorder the terms:
3(-4 + x)(x + -4) = 15

Reorder the terms:
3(-4 + x)(-4 + x) = 15

Multiply (-4 + x) * (-4 + x)
3(-4(-4 + x) + x(-4 + x)) = 15
3((-4 * -4 + x * -4) + x(-4 + x)) = 15
3((16 + -4x) + x(-4 + x)) = 15
3(16 + -4x + (-4 * x + x * x)) = 15
3(16 + -4x + (-4x + x2)) = 15

Combine like terms: -4x + -4x = -8x
3(16 + -8x + x2) = 15
(16 * 3 + -8x * 3 + x2 * 3) = 15
(48 + -24x + 3x2) = 15

Solving
48 + -24x + 3x2 = 15

Solving for variable 'x'.

Reorder the terms:
48 + -15 + -24x + 3x2 = 15 + -15

Combine like terms: 48 + -15 = 33
33 + -24x + 3x2 = 15 + -15

Combine like terms: 15 + -15 = 0
33 + -24x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(11 + -8x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(11 + -8x + x2)' equal to zero and attempt to solve:

Simplifying
11 + -8x + x2 = 0

Solving
11 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + -8x + -11 + x2 = 0 + -11

Reorder the terms:
11 + -11 + -8x + x2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -8x + x2 = 0 + -11
-8x + x2 = 0 + -11

Combine like terms: 0 + -11 = -11
-8x + x2 = -11

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 = -11 + 16

Reorder the terms:
16 + -8x + x2 = -11 + 16

Combine like terms: -11 + 16 = 5
16 + -8x + x2 = 5

Factor a perfect square on the left side:
(x + -4)(x + -4) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(x + -4) equal to 2.236067978 and -2.236067978.


Subproblem 1
x + -4 = 2.236067978

Simplifying
x + -4 = 2.236067978

Reorder the terms:
-4 + x = 2.236067978

Solving
-4 + x = 2.236067978

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 = 2.236067978 + 4

Combine like terms: -4 + 4 = 0
0 + x = 2.236067978 + 4
x = 2.236067978 + 4

Combine like terms: 2.236067978 + 4 = 6.236067978
x = 6.236067978

Simplifying
x = 6.236067978


Subproblem 2
x + -4 = -2.236067978

Simplifying
x + -4 = -2.236067978

Reorder the terms:
-4 + x = -2.236067978

Solving
-4 + x = -2.236067978

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 = -2.236067978 + 4

Combine like terms: -4 + 4 = 0
0 + x = -2.236067978 + 4
x = -2.236067978 + 4

Combine like terms: -2.236067978 + 4 = 1.763932022
x = 1.763932022

Simplifying
x = 1.763932022


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.236067978, 1.763932022}
Solution
x = {6.236067978, 1.763932022}

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