(x+2)(x+4)-20=x

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Solution for (x+2)(x+4)-20=x equation:


Simplifying
(x + 2)(x + 4) + -20 = x

Reorder the terms:
(2 + x)(x + 4) + -20 = x

Reorder the terms:
(2 + x)(4 + x) + -20 = x

Multiply (2 + x) * (4 + x)
(2(4 + x) + x(4 + x)) + -20 = x
((4 * 2 + x * 2) + x(4 + x)) + -20 = x
((8 + 2x) + x(4 + x)) + -20 = x
(8 + 2x + (4 * x + x * x)) + -20 = x
(8 + 2x + (4x + x2)) + -20 = x

Combine like terms: 2x + 4x = 6x
(8 + 6x + x2) + -20 = x

Reorder the terms:
8 + -20 + 6x + x2 = x

Combine like terms: 8 + -20 = -12
-12 + 6x + x2 = x

Solving
-12 + 6x + x2 = x

Solving for variable 'x'.

Reorder the terms:
-12 + 6x + -1x + x2 = x + -1x

Combine like terms: 6x + -1x = 5x
-12 + 5x + x2 = x + -1x

Combine like terms: x + -1x = 0
-12 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 5x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + 5x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 5x + x2 = 0 + 12
5x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
5x + x2 = 12

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 12 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 12 + 6.25

Combine like terms: 12 + 6.25 = 18.25
6.25 + 5x + x2 = 18.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(x + 2.5) equal to 4.272001873 and -4.272001873.

Subproblem 1

x + 2.5 = 4.272001873 Simplifying x + 2.5 = 4.272001873 Reorder the terms: 2.5 + x = 4.272001873 Solving 2.5 + x = 4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 4.272001873 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 4.272001873 + -2.5 x = 4.272001873 + -2.5 Combine like terms: 4.272001873 + -2.5 = 1.772001873 x = 1.772001873 Simplifying x = 1.772001873

Subproblem 2

x + 2.5 = -4.272001873 Simplifying x + 2.5 = -4.272001873 Reorder the terms: 2.5 + x = -4.272001873 Solving 2.5 + x = -4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -4.272001873 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -4.272001873 + -2.5 x = -4.272001873 + -2.5 Combine like terms: -4.272001873 + -2.5 = -6.772001873 x = -6.772001873 Simplifying x = -6.772001873

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.772001873, -6.772001873}

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