(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

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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