(x+2)(x+2)-(x+5)=5-4x

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Solution for (x+2)(x+2)-(x+5)=5-4x equation:


Simplifying
(x + 2)(x + 2) + -1(x + 5) = 5 + -4x

Reorder the terms:
(2 + x)(x + 2) + -1(x + 5) = 5 + -4x

Reorder the terms:
(2 + x)(2 + x) + -1(x + 5) = 5 + -4x

Multiply (2 + x) * (2 + x)
(2(2 + x) + x(2 + x)) + -1(x + 5) = 5 + -4x
((2 * 2 + x * 2) + x(2 + x)) + -1(x + 5) = 5 + -4x
((4 + 2x) + x(2 + x)) + -1(x + 5) = 5 + -4x
(4 + 2x + (2 * x + x * x)) + -1(x + 5) = 5 + -4x
(4 + 2x + (2x + x2)) + -1(x + 5) = 5 + -4x

Combine like terms: 2x + 2x = 4x
(4 + 4x + x2) + -1(x + 5) = 5 + -4x

Reorder the terms:
4 + 4x + x2 + -1(5 + x) = 5 + -4x
4 + 4x + x2 + (5 * -1 + x * -1) = 5 + -4x
4 + 4x + x2 + (-5 + -1x) = 5 + -4x

Reorder the terms:
4 + -5 + 4x + -1x + x2 = 5 + -4x

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

Combine like terms: 4x + -1x = 3x
-1 + 3x + x2 = 5 + -4x

Solving
-1 + 3x + x2 = 5 + -4x

Solving for variable 'x'.

Reorder the terms:
-1 + -5 + 3x + 4x + x2 = 5 + -4x + -5 + 4x

Combine like terms: -1 + -5 = -6
-6 + 3x + 4x + x2 = 5 + -4x + -5 + 4x

Combine like terms: 3x + 4x = 7x
-6 + 7x + x2 = 5 + -4x + -5 + 4x

Reorder the terms:
-6 + 7x + x2 = 5 + -5 + -4x + 4x

Combine like terms: 5 + -5 = 0
-6 + 7x + x2 = 0 + -4x + 4x
-6 + 7x + x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
-6 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 7x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + 7x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 7x + x2 = 0 + 6
7x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
7x + x2 = 6

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 6 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 6 + 12.25

Combine like terms: 6 + 12.25 = 18.25
12.25 + 7x + x2 = 18.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(x + 3.5) equal to 4.272001873 and -4.272001873.

Subproblem 1

x + 3.5 = 4.272001873 Simplifying x + 3.5 = 4.272001873 Reorder the terms: 3.5 + x = 4.272001873 Solving 3.5 + x = 4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 4.272001873 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 4.272001873 + -3.5 x = 4.272001873 + -3.5 Combine like terms: 4.272001873 + -3.5 = 0.772001873 x = 0.772001873 Simplifying x = 0.772001873

Subproblem 2

x + 3.5 = -4.272001873 Simplifying x + 3.5 = -4.272001873 Reorder the terms: 3.5 + x = -4.272001873 Solving 3.5 + x = -4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -4.272001873 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -4.272001873 + -3.5 x = -4.272001873 + -3.5 Combine like terms: -4.272001873 + -3.5 = -7.772001873 x = -7.772001873 Simplifying x = -7.772001873

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.772001873, -7.772001873}

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