(x^2)-x-0.16=0

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Solution for (x^2)-x-0.16=0 equation:


Simplifying
(x2) + -1x + -0.16 = 0
x2 + -1x + -0.16 = 0

Reorder the terms:
-0.16 + -1x + x2 = 0

Solving
-0.16 + -1x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.16' to each side of the equation.
-0.16 + -1x + 0.16 + x2 = 0 + 0.16

Reorder the terms:
-0.16 + 0.16 + -1x + x2 = 0 + 0.16

Combine like terms: -0.16 + 0.16 = 0.00
0.00 + -1x + x2 = 0 + 0.16
-1x + x2 = 0 + 0.16

Combine like terms: 0 + 0.16 = 0.16
-1x + x2 = 0.16

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 0.16 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 0.16 + 0.25

Combine like terms: 0.16 + 0.25 = 0.41
0.25 + -1x + x2 = 0.41

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 0.41

Calculate the square root of the right side: 0.640312424

Break this problem into two subproblems by setting 
(x + -0.5) equal to 0.640312424 and -0.640312424.

Subproblem 1

x + -0.5 = 0.640312424 Simplifying x + -0.5 = 0.640312424 Reorder the terms: -0.5 + x = 0.640312424 Solving -0.5 + x = 0.640312424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.640312424 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.640312424 + 0.5 x = 0.640312424 + 0.5 Combine like terms: 0.640312424 + 0.5 = 1.140312424 x = 1.140312424 Simplifying x = 1.140312424

Subproblem 2

x + -0.5 = -0.640312424 Simplifying x + -0.5 = -0.640312424 Reorder the terms: -0.5 + x = -0.640312424 Solving -0.5 + x = -0.640312424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.640312424 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.640312424 + 0.5 x = -0.640312424 + 0.5 Combine like terms: -0.640312424 + 0.5 = -0.140312424 x = -0.140312424 Simplifying x = -0.140312424

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.140312424, -0.140312424}

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