(x-4)(x-4)-5=0

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Solution for (x-4)(x-4)-5=0 equation:


Simplifying
(x + -4)(x + -4) + -5 = 0

Reorder the terms:
(-4 + x)(x + -4) + -5 = 0

Reorder the terms:
(-4 + x)(-4 + x) + -5 = 0

Multiply (-4 + x) * (-4 + x)
(-4(-4 + x) + x(-4 + x)) + -5 = 0
((-4 * -4 + x * -4) + x(-4 + x)) + -5 = 0
((16 + -4x) + x(-4 + x)) + -5 = 0
(16 + -4x + (-4 * x + x * x)) + -5 = 0
(16 + -4x + (-4x + x2)) + -5 = 0

Combine like terms: -4x + -4x = -8x
(16 + -8x + x2) + -5 = 0

Reorder the terms:
16 + -5 + -8x + x2 = 0

Combine like terms: 16 + -5 = 11
11 + -8x + x2 = 0

Solving
11 + -8x + x2 = 0

Solving for variable 'x'.

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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