(.1+x)(.1+x)=3(.01-x)

Solution for (.1+x)(.1+x)=3(.01-x) equation:

Simplifying
(0.1 + x)(0.1 + x) = 3(0.01 + -1x)

Multiply (0.1 + x) * (0.1 + x)
(0.1(0.1 + x) + x(0.1 + x)) = 3(0.01 + -1x)
((0.1 * 0.1 + x * 0.1) + x(0.1 + x)) = 3(0.01 + -1x)
((0.01 + 0.1x) + x(0.1 + x)) = 3(0.01 + -1x)
(0.01 + 0.1x + (0.1 * x + x * x)) = 3(0.01 + -1x)
(0.01 + 0.1x + (0.1x + x2)) = 3(0.01 + -1x)

Combine like terms: 0.1x + 0.1x = 0.2x
(0.01 + 0.2x + x2) = 3(0.01 + -1x)
0.01 + 0.2x + x2 = (0.01 * 3 + -1x * 3)
0.01 + 0.2x + x2 = (0.03 + -3x)

Solving
0.01 + 0.2x + x2 = 0.03 + -3x

Solving for variable 'x'.

Reorder the terms:
0.01 + -0.03 + 0.2x + 3x + x2 = 0.03 + -3x + -0.03 + 3x

Combine like terms: 0.01 + -0.03 = -0.02
-0.02 + 0.2x + 3x + x2 = 0.03 + -3x + -0.03 + 3x

Combine like terms: 0.2x + 3x = 3.2x
-0.02 + 3.2x + x2 = 0.03 + -3x + -0.03 + 3x

Reorder the terms:
-0.02 + 3.2x + x2 = 0.03 + -0.03 + -3x + 3x

Combine like terms: 0.03 + -0.03 = 0.00
-0.02 + 3.2x + x2 = 0.00 + -3x + 3x
-0.02 + 3.2x + x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
-0.02 + 3.2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '0.02' to each side of the equation.
-0.02 + 3.2x + 0.02 + x2 = 0 + 0.02

Reorder the terms:
-0.02 + 0.02 + 3.2x + x2 = 0 + 0.02

Combine like terms: -0.02 + 0.02 = 0.00
0.00 + 3.2x + x2 = 0 + 0.02
3.2x + x2 = 0 + 0.02

Combine like terms: 0 + 0.02 = 0.02
3.2x + x2 = 0.02

The x term is 3.2x.  Take half its coefficient (1.6).
Square it (2.56) and add it to both sides.

Add '2.56' to each side of the equation.
3.2x + 2.56 + x2 = 0.02 + 2.56

Reorder the terms:
2.56 + 3.2x + x2 = 0.02 + 2.56

Combine like terms: 0.02 + 2.56 = 2.58
2.56 + 3.2x + x2 = 2.58

Factor a perfect square on the left side:
(x + 1.6)(x + 1.6) = 2.58

Calculate the square root of the right side: 1.60623784

Break this problem into two subproblems by setting 
(x + 1.6) equal to 1.60623784 and -1.60623784.

Subproblem 1
x + 1.6 = 1.60623784

Simplifying
x + 1.6 = 1.60623784

Reorder the terms:
1.6 + x = 1.60623784

Solving
1.6 + x = 1.60623784

Solving for variable 'x'.

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

Add '-1.6' to each side of the equation.
1.6 + -1.6 + x = 1.60623784 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + x = 1.60623784 + -1.6
x = 1.60623784 + -1.6

Combine like terms: 1.60623784 + -1.6 = 0.00623784
x = 0.00623784

Simplifying
x = 0.00623784

Subproblem 2
x + 1.6 = -1.60623784

Simplifying
x + 1.6 = -1.60623784

Reorder the terms:
1.6 + x = -1.60623784

Solving
1.6 + x = -1.60623784

Solving for variable 'x'.

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

Add '-1.6' to each side of the equation.
1.6 + -1.6 + x = -1.60623784 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + x = -1.60623784 + -1.6
x = -1.60623784 + -1.6

Combine like terms: -1.60623784 + -1.6 = -3.20623784
x = -3.20623784

Simplifying
x = -3.20623784

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.00623784, -3.20623784}