(x+1)(x+2)=18

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Solution for (x+1)(x+2)=18 equation:


Simplifying
(x + 1)(x + 2) = 18

Reorder the terms:
(1 + x)(x + 2) = 18

Reorder the terms:
(1 + x)(2 + x) = 18

Multiply (1 + x) * (2 + x)
(1(2 + x) + x(2 + x)) = 18
((2 * 1 + x * 1) + x(2 + x)) = 18
((2 + 1x) + x(2 + x)) = 18
(2 + 1x + (2 * x + x * x)) = 18
(2 + 1x + (2x + x2)) = 18

Combine like terms: 1x + 2x = 3x
(2 + 3x + x2) = 18

Solving
2 + 3x + x2 = 18

Solving for variable 'x'.

Reorder the terms:
2 + -18 + 3x + x2 = 18 + -18

Combine like terms: 2 + -18 = -16
-16 + 3x + x2 = 18 + -18

Combine like terms: 18 + -18 = 0
-16 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 3x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + 3x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 3x + x2 = 0 + 16
3x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
3x + x2 = 16

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 16 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 16 + 2.25

Combine like terms: 16 + 2.25 = 18.25
2.25 + 3x + x2 = 18.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(x + 1.5) equal to 4.272001873 and -4.272001873.

Subproblem 1

x + 1.5 = 4.272001873 Simplifying x + 1.5 = 4.272001873 Reorder the terms: 1.5 + x = 4.272001873 Solving 1.5 + x = 4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 4.272001873 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 4.272001873 + -1.5 x = 4.272001873 + -1.5 Combine like terms: 4.272001873 + -1.5 = 2.772001873 x = 2.772001873 Simplifying x = 2.772001873

Subproblem 2

x + 1.5 = -4.272001873 Simplifying x + 1.5 = -4.272001873 Reorder the terms: 1.5 + x = -4.272001873 Solving 1.5 + x = -4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -4.272001873 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -4.272001873 + -1.5 x = -4.272001873 + -1.5 Combine like terms: -4.272001873 + -1.5 = -5.772001873 x = -5.772001873 Simplifying x = -5.772001873

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.772001873, -5.772001873}

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