1.15=(1+x)(1+x)

Solution for 1.15=(1+x)(1+x) equation:

Simplifying
1.15 = (1 + x)(1 + x)

Multiply (1 + x) * (1 + x)
1.15 = (1(1 + x) + x(1 + x))
1.15 = ((1 * 1 + x * 1) + x(1 + x))
1.15 = ((1 + 1x) + x(1 + x))
1.15 = (1 + 1x + (1 * x + x * x))
1.15 = (1 + 1x + (1x + x2))

Combine like terms: 1x + 1x = 2x
1.15 = (1 + 2x + x2)

Solving
1.15 = 1 + 2x + x2

Solving for variable 'x'.

Combine like terms: 1.15 + -1 = 0.15
0.15 + -2x + -1x2 = 1 + 2x + x2 + -1 + -2x + -1x2

Reorder the terms:
0.15 + -2x + -1x2 = 1 + -1 + 2x + -2x + x2 + -1x2

Combine like terms: 1 + -1 = 0
0.15 + -2x + -1x2 = 0 + 2x + -2x + x2 + -1x2
0.15 + -2x + -1x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
0.15 + -2x + -1x2 = 0 + x2 + -1x2
0.15 + -2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
0.15 + -2x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-0.15 + 2x + x2 = 0

Move the constant term to the right:

Add '0.15' to each side of the equation.
-0.15 + 2x + 0.15 + x2 = 0 + 0.15

Reorder the terms:
-0.15 + 0.15 + 2x + x2 = 0 + 0.15

Combine like terms: -0.15 + 0.15 = 0.00
0.00 + 2x + x2 = 0 + 0.15
2x + x2 = 0 + 0.15

Combine like terms: 0 + 0.15 = 0.15
2x + x2 = 0.15

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 = 0.15 + 1

Reorder the terms:
1 + 2x + x2 = 0.15 + 1

Combine like terms: 0.15 + 1 = 1.15
1 + 2x + x2 = 1.15

Factor a perfect square on the left side:
(x + 1)(x + 1) = 1.15

Calculate the square root of the right side: 1.072380529

Break this problem into two subproblems by setting 
(x + 1) equal to 1.072380529 and -1.072380529.

Subproblem 1
x + 1 = 1.072380529

Simplifying
x + 1 = 1.072380529

Reorder the terms:
1 + x = 1.072380529

Solving
1 + x = 1.072380529

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 = 1.072380529 + -1

Combine like terms: 1 + -1 = 0
0 + x = 1.072380529 + -1
x = 1.072380529 + -1

Combine like terms: 1.072380529 + -1 = 0.072380529
x = 0.072380529

Simplifying
x = 0.072380529

Subproblem 2
x + 1 = -1.072380529

Simplifying
x + 1 = -1.072380529

Reorder the terms:
1 + x = -1.072380529

Solving
1 + x = -1.072380529

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 = -1.072380529 + -1

Combine like terms: 1 + -1 = 0
0 + x = -1.072380529 + -1
x = -1.072380529 + -1

Combine like terms: -1.072380529 + -1 = -2.072380529
x = -2.072380529

Simplifying
x = -2.072380529

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.072380529, -2.072380529}