[(x-4)(x-4)]=5

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Solution for [(x-4)(x-4)]=5 equation: 


Simplifying
[(x + -4)(x + -4)] = 5

Reorder the terms:
[(-4 + x)(x + -4)] = 5

Reorder the terms:
[(-4 + x)(-4 + x)] = 5

Multiply (-4 + x) * (-4 + x)
[(-4(-4 + x) + x(-4 + x))] = 5
[((-4 * -4 + x * -4) + x(-4 + x))] = 5
[((16 + -4x) + x(-4 + x))] = 5
[(16 + -4x + (-4 * x + x * x))] = 5
[(16 + -4x + (-4x + x2))] = 5

Combine like terms: -4x + -4x = -8x
[(16 + -8x + x2)] = 5
[16 + -8x + x2] = 5

Remove brackets around [16 + -8x + x2]
16 + -8x + x2 = 5

Solving
16 + -8x + x2 = 5

Solving for variable 'x'.

Reorder the terms:
16 + -5 + -8x + x2 = 5 + -5

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

Combine like terms: 5 + -5 = 0
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}

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