1=(0.02*.02)+2*(0.02x)+(x*x)

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Solution for 1=(0.02*.02)+2*(0.02x)+(x*x) equation: 


Simplifying
1 = (0.02 * 0.02) + 2(0.02x) + (x * x)

Multiply 0.02 * 0.02
1 = (0.0004) + 2(0.02x) + (x * x)
1 = 0.0004 + 2(0.02x) + (x * x)

Remove parenthesis around (0.02x)
1 = 0.0004 + 2 * 0.02x + (x * x)

Multiply 2 * 0.02
1 = 0.0004 + 0.04x + (x * x)

Multiply x * x
1 = 0.0004 + 0.04x + (x2)
1 = 0.0004 + 0.04x + x2

Solving
1 = 0.0004 + 0.04x + x2

Solving for variable 'x'.

Combine like terms: 1 + -0.0004 = 0.9996
0.9996 + -0.04x + -1x2 = 0.0004 + 0.04x + x2 + -0.0004 + -0.04x + -1x2

Reorder the terms:
0.9996 + -0.04x + -1x2 = 0.0004 + -0.0004 + 0.04x + -0.04x + x2 + -1x2

Combine like terms: 0.0004 + -0.0004 = 0.0000
0.9996 + -0.04x + -1x2 = 0.0000 + 0.04x + -0.04x + x2 + -1x2
0.9996 + -0.04x + -1x2 = 0.04x + -0.04x + x2 + -1x2

Combine like terms: 0.04x + -0.04x = 0.00
0.9996 + -0.04x + -1x2 = 0.00 + x2 + -1x2
0.9996 + -0.04x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
0.9996 + -0.04x + -1x2 = 0

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

Divide each side by '-1'.
-0.9996 + 0.04x + x2 = 0

Move the constant term to the right:

Add '0.9996' to each side of the equation.
-0.9996 + 0.04x + 0.9996 + x2 = 0 + 0.9996

Reorder the terms:
-0.9996 + 0.9996 + 0.04x + x2 = 0 + 0.9996

Combine like terms: -0.9996 + 0.9996 = 0.0000
0.0000 + 0.04x + x2 = 0 + 0.9996
0.04x + x2 = 0 + 0.9996

Combine like terms: 0 + 0.9996 = 0.9996
0.04x + x2 = 0.9996

The x term is 0.04x.  Take half its coefficient (0.02).
Square it (0.0004) and add it to both sides.

Add '0.0004' to each side of the equation.
0.04x + 0.0004 + x2 = 0.9996 + 0.0004

Reorder the terms:
0.0004 + 0.04x + x2 = 0.9996 + 0.0004

Combine like terms: 0.9996 + 0.0004 = 1
0.0004 + 0.04x + x2 = 1

Factor a perfect square on the left side:
(x + 0.02)(x + 0.02) = 1

Calculate the square root of the right side: 1

Break this problem into two subproblems by setting 
(x + 0.02) equal to 1 and -1.


Subproblem 1
x + 0.02 = 1

Simplifying
x + 0.02 = 1

Reorder the terms:
0.02 + x = 1

Solving
0.02 + x = 1

Solving for variable 'x'.

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

Add '-0.02' to each side of the equation.
0.02 + -0.02 + x = 1 + -0.02

Combine like terms: 0.02 + -0.02 = 0.00
0.00 + x = 1 + -0.02
x = 1 + -0.02

Combine like terms: 1 + -0.02 = 0.98
x = 0.98

Simplifying
x = 0.98


Subproblem 2
x + 0.02 = -1

Simplifying
x + 0.02 = -1

Reorder the terms:
0.02 + x = -1

Solving
0.02 + x = -1

Solving for variable 'x'.

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

Add '-0.02' to each side of the equation.
0.02 + -0.02 + x = -1 + -0.02

Combine like terms: 0.02 + -0.02 = 0.00
0.00 + x = -1 + -0.02
x = -1 + -0.02

Combine like terms: -1 + -0.02 = -1.02
x = -1.02

Simplifying
x = -1.02


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.98, -1.02}

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