x+(x+1)(x+2)=138

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Solution for x+(x+1)(x+2)=138 equation:


Simplifying
x + (x + 1)(x + 2) = 138

Reorder the terms:
x + (1 + x)(x + 2) = 138

Reorder the terms:
x + (1 + x)(2 + x) = 138

Multiply (1 + x) * (2 + x)
x + (1(2 + x) + x(2 + x)) = 138
x + ((2 * 1 + x * 1) + x(2 + x)) = 138
x + ((2 + 1x) + x(2 + x)) = 138
x + (2 + 1x + (2 * x + x * x)) = 138
x + (2 + 1x + (2x + x2)) = 138

Combine like terms: 1x + 2x = 3x
x + (2 + 3x + x2) = 138

Reorder the terms:
2 + x + 3x + x2 = 138

Combine like terms: x + 3x = 4x
2 + 4x + x2 = 138

Solving
2 + 4x + x2 = 138

Solving for variable 'x'.

Reorder the terms:
2 + -138 + 4x + x2 = 138 + -138

Combine like terms: 2 + -138 = -136
-136 + 4x + x2 = 138 + -138

Combine like terms: 138 + -138 = 0
-136 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '136' to each side of the equation.
-136 + 4x + 136 + x2 = 0 + 136

Reorder the terms:
-136 + 136 + 4x + x2 = 0 + 136

Combine like terms: -136 + 136 = 0
0 + 4x + x2 = 0 + 136
4x + x2 = 0 + 136

Combine like terms: 0 + 136 = 136
4x + x2 = 136

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 = 136 + 4

Reorder the terms:
4 + 4x + x2 = 136 + 4

Combine like terms: 136 + 4 = 140
4 + 4x + x2 = 140

Factor a perfect square on the left side:
(x + 2)(x + 2) = 140

Calculate the square root of the right side: 11.832159566

Break this problem into two subproblems by setting 
(x + 2) equal to 11.832159566 and -11.832159566.

Subproblem 1

x + 2 = 11.832159566 Simplifying x + 2 = 11.832159566 Reorder the terms: 2 + x = 11.832159566 Solving 2 + x = 11.832159566 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 = 11.832159566 + -2 Combine like terms: 2 + -2 = 0 0 + x = 11.832159566 + -2 x = 11.832159566 + -2 Combine like terms: 11.832159566 + -2 = 9.832159566 x = 9.832159566 Simplifying x = 9.832159566

Subproblem 2

x + 2 = -11.832159566 Simplifying x + 2 = -11.832159566 Reorder the terms: 2 + x = -11.832159566 Solving 2 + x = -11.832159566 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 = -11.832159566 + -2 Combine like terms: 2 + -2 = 0 0 + x = -11.832159566 + -2 x = -11.832159566 + -2 Combine like terms: -11.832159566 + -2 = -13.832159566 x = -13.832159566 Simplifying x = -13.832159566

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.832159566, -13.832159566}

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