4.24(0.10-x)(0.10-x)=x*x

Solution for 4.24(0.10-x)(0.10-x)=x*x equation:

Simplifying
4.24(0.10 + -1x)(0.10 + -1x) = x * x

Multiply (0.10 + -1x) * (0.10 + -1x)
4.24(0.10(0.10 + -1x) + -1x * (0.10 + -1x)) = x * x
4.24((0.10 * 0.10 + -1x * 0.10) + -1x * (0.10 + -1x)) = x * x
4.24((0.01 + -0.1x) + -1x * (0.10 + -1x)) = x * x
4.24(0.01 + -0.1x + (0.10 * -1x + -1x * -1x)) = x * x
4.24(0.01 + -0.1x + (-0.1x + 1x2)) = x * x

Combine like terms: -0.1x + -0.1x = -0.2x
4.24(0.01 + -0.2x + 1x2) = x * x
(0.01 * 4.24 + -0.2x * 4.24 + 1x2 * 4.24) = x * x
(0.0424 + -0.848x + 4.24x2) = x * x

Multiply x * x
0.0424 + -0.848x + 4.24x2 = x2

Solving
0.0424 + -0.848x + 4.24x2 = x2

Solving for variable 'x'.

Combine like terms: 4.24x2 + -1x2 = 3.24x2
0.0424 + -0.848x + 3.24x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
0.0424 + -0.848x + 3.24x2 = 0

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

Divide each side by '3.24'.
0.01308641975 + -0.2617283951x + x2 = 0

Move the constant term to the right:

Add '-0.01308641975' to each side of the equation.
0.01308641975 + -0.2617283951x + -0.01308641975 + x2 = 0 + -0.01308641975

Reorder the terms:
0.01308641975 + -0.01308641975 + -0.2617283951x + x2 = 0 + -0.01308641975

Combine like terms: 0.01308641975 + -0.01308641975 = 0.00000000000
0.00000000000 + -0.2617283951x + x2 = 0 + -0.01308641975
-0.2617283951x + x2 = 0 + -0.01308641975

Combine like terms: 0 + -0.01308641975 = -0.01308641975
-0.2617283951x + x2 = -0.01308641975

The x term is -0.2617283951x.  Take half its coefficient (-0.1308641976).
Square it (0.01712543821) and add it to both sides.

Add '0.01712543821' to each side of the equation.
-0.2617283951x + 0.01712543821 + x2 = -0.01308641975 + 0.01712543821

Reorder the terms:
0.01712543821 + -0.2617283951x + x2 = -0.01308641975 + 0.01712543821

Combine like terms: -0.01308641975 + 0.01712543821 = 0.00403901846
0.01712543821 + -0.2617283951x + x2 = 0.00403901846

Factor a perfect square on the left side:
(x + -0.1308641976)(x + -0.1308641976) = 0.00403901846

Calculate the square root of the right side: 0.063553273

Break this problem into two subproblems by setting 
(x + -0.1308641976) equal to 0.063553273 and -0.063553273.

Subproblem 1
x + -0.1308641976 = 0.063553273

Simplifying
x + -0.1308641976 = 0.063553273

Reorder the terms:
-0.1308641976 + x = 0.063553273

Solving
-0.1308641976 + x = 0.063553273

Solving for variable 'x'.

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

Add '0.1308641976' to each side of the equation.
-0.1308641976 + 0.1308641976 + x = 0.063553273 + 0.1308641976

Combine like terms: -0.1308641976 + 0.1308641976 = 0.0000000000
0.0000000000 + x = 0.063553273 + 0.1308641976
x = 0.063553273 + 0.1308641976

Combine like terms: 0.063553273 + 0.1308641976 = 0.1944174706
x = 0.1944174706

Simplifying
x = 0.1944174706

Subproblem 2
x + -0.1308641976 = -0.063553273

Simplifying
x + -0.1308641976 = -0.063553273

Reorder the terms:
-0.1308641976 + x = -0.063553273

Solving
-0.1308641976 + x = -0.063553273

Solving for variable 'x'.

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

Add '0.1308641976' to each side of the equation.
-0.1308641976 + 0.1308641976 + x = -0.063553273 + 0.1308641976

Combine like terms: -0.1308641976 + 0.1308641976 = 0.0000000000
0.0000000000 + x = -0.063553273 + 0.1308641976
x = -0.063553273 + 0.1308641976

Combine like terms: -0.063553273 + 0.1308641976 = 0.0673109246
x = 0.0673109246

Simplifying
x = 0.0673109246

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.1944174706, 0.0673109246}