x+x(x+1)=1.10

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Solution for x+x(x+1)=1.10 equation: 


Simplifying
x + x(x + 1) = 1.10

Reorder the terms:
x + x(1 + x) = 1.10
x + (1 * x + x * x) = 1.10
x + (1x + x2) = 1.10

Combine like terms: x + 1x = 2x
2x + x2 = 1.10

Solving
2x + x2 = 1.10

Solving for variable 'x'.

Reorder the terms:
-1.10 + 2x + x2 = 1.10 + -1.10

Combine like terms: 1.10 + -1.10 = 0.00
-1.10 + 2x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '1.10' to each side of the equation.
-1.10 + 2x + 1.10 + x2 = 0.00 + 1.10

Reorder the terms:
-1.10 + 1.10 + 2x + x2 = 0.00 + 1.10

Combine like terms: -1.10 + 1.10 = 0.00
0.00 + 2x + x2 = 0.00 + 1.10
2x + x2 = 0.00 + 1.10

Combine like terms: 0.00 + 1.10 = 1.1
2x + x2 = 1.1

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 1.1 + 1

Reorder the terms:
1 + 2x + x2 = 1.1 + 1

Combine like terms: 1.1 + 1 = 2.1
1 + 2x + x2 = 2.1

Factor a perfect square on the left side:
(x + 1)(x + 1) = 2.1

Calculate the square root of the right side: 1.449137675

Break this problem into two subproblems by setting 
(x + 1) equal to 1.449137675 and -1.449137675.


Subproblem 1
x + 1 = 1.449137675

Simplifying
x + 1 = 1.449137675

Reorder the terms:
1 + x = 1.449137675

Solving
1 + x = 1.449137675

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + x = 1.449137675 + -1

Combine like terms: 1 + -1 = 0
0 + x = 1.449137675 + -1
x = 1.449137675 + -1

Combine like terms: 1.449137675 + -1 = 0.449137675
x = 0.449137675

Simplifying
x = 0.449137675


Subproblem 2
x + 1 = -1.449137675

Simplifying
x + 1 = -1.449137675

Reorder the terms:
1 + x = -1.449137675

Solving
1 + x = -1.449137675

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + x = -1.449137675 + -1

Combine like terms: 1 + -1 = 0
0 + x = -1.449137675 + -1
x = -1.449137675 + -1

Combine like terms: -1.449137675 + -1 = -2.449137675
x = -2.449137675

Simplifying
x = -2.449137675


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.449137675, -2.449137675}

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