.52=(.050+x)*(.040+x)

Solution for .52=(.050+x)*(.040+x) equation:

Simplifying
0.52 = (0.050 + x)(0.040 + x)

Multiply (0.050 + x) * (0.040 + x)
0.52 = (0.050(0.040 + x) + x(0.040 + x))
0.52 = ((0.040 * 0.050 + x * 0.050) + x(0.040 + x))
0.52 = ((0.002 + 0.050x) + x(0.040 + x))
0.52 = (0.002 + 0.050x + (0.040 * x + x * x))
0.52 = (0.002 + 0.050x + (0.040x + x2))

Combine like terms: 0.050x + 0.040x = 0.09x
0.52 = (0.002 + 0.09x + x2)

Solving
0.52 = 0.002 + 0.09x + x2

Solving for variable 'x'.

Combine like terms: 0.52 + -0.002 = 0.518
0.518 + -0.09x + -1x2 = 0.002 + 0.09x + x2 + -0.002 + -0.09x + -1x2

Reorder the terms:
0.518 + -0.09x + -1x2 = 0.002 + -0.002 + 0.09x + -0.09x + x2 + -1x2

Combine like terms: 0.002 + -0.002 = 0.000
0.518 + -0.09x + -1x2 = 0.000 + 0.09x + -0.09x + x2 + -1x2
0.518 + -0.09x + -1x2 = 0.09x + -0.09x + x2 + -1x2

Combine like terms: 0.09x + -0.09x = 0.00
0.518 + -0.09x + -1x2 = 0.00 + x2 + -1x2
0.518 + -0.09x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
0.518 + -0.09x + -1x2 = 0

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

Divide each side by '-1'.
-0.518 + 0.09x + x2 = 0

Move the constant term to the right:

Add '0.518' to each side of the equation.
-0.518 + 0.09x + 0.518 + x2 = 0 + 0.518

Reorder the terms:
-0.518 + 0.518 + 0.09x + x2 = 0 + 0.518

Combine like terms: -0.518 + 0.518 = 0.000
0.000 + 0.09x + x2 = 0 + 0.518
0.09x + x2 = 0 + 0.518

Combine like terms: 0 + 0.518 = 0.518
0.09x + x2 = 0.518

The x term is 0.09x.  Take half its coefficient (0.045).
Square it (0.002025) and add it to both sides.

Add '0.002025' to each side of the equation.
0.09x + 0.002025 + x2 = 0.518 + 0.002025

Reorder the terms:
0.002025 + 0.09x + x2 = 0.518 + 0.002025

Combine like terms: 0.518 + 0.002025 = 0.520025
0.002025 + 0.09x + x2 = 0.520025

Factor a perfect square on the left side:
(x + 0.045)(x + 0.045) = 0.520025

Calculate the square root of the right side: 0.721127589

Break this problem into two subproblems by setting 
(x + 0.045) equal to 0.721127589 and -0.721127589.

Subproblem 1
x + 0.045 = 0.721127589

Simplifying
x + 0.045 = 0.721127589

Reorder the terms:
0.045 + x = 0.721127589

Solving
0.045 + x = 0.721127589

Solving for variable 'x'.

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

Add '-0.045' to each side of the equation.
0.045 + -0.045 + x = 0.721127589 + -0.045

Combine like terms: 0.045 + -0.045 = 0.000
0.000 + x = 0.721127589 + -0.045
x = 0.721127589 + -0.045

Combine like terms: 0.721127589 + -0.045 = 0.676127589
x = 0.676127589

Simplifying
x = 0.676127589

Subproblem 2
x + 0.045 = -0.721127589

Simplifying
x + 0.045 = -0.721127589

Reorder the terms:
0.045 + x = -0.721127589

Solving
0.045 + x = -0.721127589

Solving for variable 'x'.

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

Add '-0.045' to each side of the equation.
0.045 + -0.045 + x = -0.721127589 + -0.045

Combine like terms: 0.045 + -0.045 = 0.000
0.000 + x = -0.721127589 + -0.045
x = -0.721127589 + -0.045

Combine like terms: -0.721127589 + -0.045 = -0.766127589
x = -0.766127589

Simplifying
x = -0.766127589

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.676127589, -0.766127589}