(2+x)(2+x)=5

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Solution for (2+x)(2+x)=5 equation:


Simplifying
(2 + x)(2 + x) = 5

Multiply (2 + x) * (2 + x)
(2(2 + x) + x(2 + x)) = 5
((2 * 2 + x * 2) + x(2 + x)) = 5
((4 + 2x) + x(2 + x)) = 5
(4 + 2x + (2 * x + x * x)) = 5
(4 + 2x + (2x + x2)) = 5

Combine like terms: 2x + 2x = 4x
(4 + 4x + x2) = 5

Solving
4 + 4x + x2 = 5

Solving for variable 'x'.

Reorder the terms:
4 + -5 + 4x + x2 = 5 + -5

Combine like terms: 4 + -5 = -1
-1 + 4x + x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-1 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 4x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 4x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 4x + x2 = 0 + 1
4x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
4x + x2 = 1

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 1 + 4

Reorder the terms:
4 + 4x + x2 = 1 + 4

Combine like terms: 1 + 4 = 5
4 + 4x + x2 = 5

Factor a perfect square on the left side:
(x + 2)(x + 2) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(x + 2) equal to 2.236067978 and -2.236067978.

Subproblem 1

x + 2 = 2.236067978 Simplifying x + 2 = 2.236067978 Reorder the terms: 2 + x = 2.236067978 Solving 2 + x = 2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 2.236067978 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.236067978 + -2 x = 2.236067978 + -2 Combine like terms: 2.236067978 + -2 = 0.236067978 x = 0.236067978 Simplifying x = 0.236067978

Subproblem 2

x + 2 = -2.236067978 Simplifying x + 2 = -2.236067978 Reorder the terms: 2 + x = -2.236067978 Solving 2 + x = -2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -2.236067978 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.236067978 + -2 x = -2.236067978 + -2 Combine like terms: -2.236067978 + -2 = -4.236067978 x = -4.236067978 Simplifying x = -4.236067978

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.236067978, -4.236067978}

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