x^2-1.6x=0.04

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Solution for x^2-1.6x=0.04 equation:


Simplifying
x2 + -1.6x = 0.04

Reorder the terms:
-1.6x + x2 = 0.04

Solving
-1.6x + x2 = 0.04

Solving for variable 'x'.

Reorder the terms:
-0.04 + -1.6x + x2 = 0.04 + -0.04

Combine like terms: 0.04 + -0.04 = 0.00
-0.04 + -1.6x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '0.04' to each side of the equation.
-0.04 + -1.6x + 0.04 + x2 = 0.00 + 0.04

Reorder the terms:
-0.04 + 0.04 + -1.6x + x2 = 0.00 + 0.04

Combine like terms: -0.04 + 0.04 = 0.00
0.00 + -1.6x + x2 = 0.00 + 0.04
-1.6x + x2 = 0.00 + 0.04

Combine like terms: 0.00 + 0.04 = 0.04
-1.6x + x2 = 0.04

The x term is -1.6x.  Take half its coefficient (-0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
-1.6x + 0.64 + x2 = 0.04 + 0.64

Reorder the terms:
0.64 + -1.6x + x2 = 0.04 + 0.64

Combine like terms: 0.04 + 0.64 = 0.68
0.64 + -1.6x + x2 = 0.68

Factor a perfect square on the left side:
(x + -0.8)(x + -0.8) = 0.68

Calculate the square root of the right side: 0.824621125

Break this problem into two subproblems by setting 
(x + -0.8) equal to 0.824621125 and -0.824621125.


Subproblem 1
x + -0.8 = 0.824621125

Simplifying
x + -0.8 = 0.824621125

Reorder the terms:
-0.8 + x = 0.824621125

Solving
-0.8 + x = 0.824621125

Solving for variable 'x'.

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

Add '0.8' to each side of the equation.
-0.8 + 0.8 + x = 0.824621125 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + x = 0.824621125 + 0.8
x = 0.824621125 + 0.8

Combine like terms: 0.824621125 + 0.8 = 1.624621125
x = 1.624621125

Simplifying
x = 1.624621125


Subproblem 2
x + -0.8 = -0.824621125

Simplifying
x + -0.8 = -0.824621125

Reorder the terms:
-0.8 + x = -0.824621125

Solving
-0.8 + x = -0.824621125

Solving for variable 'x'.

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

Add '0.8' to each side of the equation.
-0.8 + 0.8 + x = -0.824621125 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + x = -0.824621125 + 0.8
x = -0.824621125 + 0.8

Combine like terms: -0.824621125 + 0.8 = -0.024621125
x = -0.024621125

Simplifying
x = -0.024621125


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.624621125, -0.024621125}

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