.04+.4x+x^2=1

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Solution for .04+.4x+x^2=1 equation:


Simplifying
0.04 + 0.4x + x2 = 1

Solving
0.04 + 0.4x + x2 = 1

Solving for variable 'x'.

Reorder the terms:
0.04 + -1 + 0.4x + x2 = 1 + -1

Combine like terms: 0.04 + -1 = -0.96
-0.96 + 0.4x + x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-0.96 + 0.4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '0.96' to each side of the equation.
-0.96 + 0.4x + 0.96 + x2 = 0 + 0.96

Reorder the terms:
-0.96 + 0.96 + 0.4x + x2 = 0 + 0.96

Combine like terms: -0.96 + 0.96 = 0.00
0.00 + 0.4x + x2 = 0 + 0.96
0.4x + x2 = 0 + 0.96

Combine like terms: 0 + 0.96 = 0.96
0.4x + x2 = 0.96

The x term is 0.4x.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4x + 0.04 + x2 = 0.96 + 0.04

Reorder the terms:
0.04 + 0.4x + x2 = 0.96 + 0.04

Combine like terms: 0.96 + 0.04 = 1
0.04 + 0.4x + x2 = 1

Factor a perfect square on the left side:
(x + 0.2)(x + 0.2) = 1

Calculate the square root of the right side: 1

Break this problem into two subproblems by setting 
(x + 0.2) equal to 1 and -1.


Subproblem 1
x + 0.2 = 1

Simplifying
x + 0.2 = 1

Reorder the terms:
0.2 + x = 1

Solving
0.2 + x = 1

Solving for variable 'x'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + x = 1 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + x = 1 + -0.2
x = 1 + -0.2

Combine like terms: 1 + -0.2 = 0.8
x = 0.8

Simplifying
x = 0.8


Subproblem 2
x + 0.2 = -1

Simplifying
x + 0.2 = -1

Reorder the terms:
0.2 + x = -1

Solving
0.2 + x = -1

Solving for variable 'x'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + x = -1 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + x = -1 + -0.2
x = -1 + -0.2

Combine like terms: -1 + -0.2 = -1.2
x = -1.2

Simplifying
x = -1.2


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.8, -1.2}

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