X^2+0.04X+0.02=1

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Solution for X^2+0.04X+0.02=1 equation: 


Simplifying
X2 + 0.04X + 0.02 = 1

Reorder the terms:
0.02 + 0.04X + X2 = 1

Solving
0.02 + 0.04X + X2 = 1

Solving for variable 'X'.

Reorder the terms:
0.02 + -1 + 0.04X + X2 = 1 + -1

Combine like terms: 0.02 + -1 = -0.98
-0.98 + 0.04X + X2 = 1 + -1

Combine like terms: 1 + -1 = 0
-0.98 + 0.04X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '0.98' to each side of the equation.
-0.98 + 0.04X + 0.98 + X2 = 0 + 0.98

Reorder the terms:
-0.98 + 0.98 + 0.04X + X2 = 0 + 0.98

Combine like terms: -0.98 + 0.98 = 0.00
0.00 + 0.04X + X2 = 0 + 0.98
0.04X + X2 = 0 + 0.98

Combine like terms: 0 + 0.98 = 0.98
0.04X + X2 = 0.98

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 = 0.98 + 0.0004

Reorder the terms:
0.0004 + 0.04X + X2 = 0.98 + 0.0004

Combine like terms: 0.98 + 0.0004 = 0.9804
0.0004 + 0.04X + X2 = 0.9804

Factor a perfect square on the left side:
(X + 0.02)(X + 0.02) = 0.9804

Calculate the square root of the right side: 0.990151504

Break this problem into two subproblems by setting 
(X + 0.02) equal to 0.990151504 and -0.990151504.


Subproblem 1
X + 0.02 = 0.990151504

Simplifying
X + 0.02 = 0.990151504

Reorder the terms:
0.02 + X = 0.990151504

Solving
0.02 + X = 0.990151504

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 = 0.990151504 + -0.02

Combine like terms: 0.02 + -0.02 = 0.00
0.00 + X = 0.990151504 + -0.02
X = 0.990151504 + -0.02

Combine like terms: 0.990151504 + -0.02 = 0.970151504
X = 0.970151504

Simplifying
X = 0.970151504


Subproblem 2
X + 0.02 = -0.990151504

Simplifying
X + 0.02 = -0.990151504

Reorder the terms:
0.02 + X = -0.990151504

Solving
0.02 + X = -0.990151504

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 = -0.990151504 + -0.02

Combine like terms: 0.02 + -0.02 = 0.00
0.00 + X = -0.990151504 + -0.02
X = -0.990151504 + -0.02

Combine like terms: -0.990151504 + -0.02 = -1.010151504
X = -1.010151504

Simplifying
X = -1.010151504


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {0.970151504, -1.010151504}

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