0.0714x^2-0.1428x=1

Solution for 0.0714x^2-0.1428x=1 equation:

Simplifying
0.0714x2 + -0.1428x = 1

Reorder the terms:
-0.1428x + 0.0714x2 = 1

Solving
-0.1428x + 0.0714x2 = 1

Solving for variable 'x'.

Reorder the terms:
-1 + -0.1428x + 0.0714x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + -0.1428x + 0.0714x2 = 0

Begin completing the square.  Divide all terms by
0.0714 the coefficient of the squared term: 

Divide each side by '0.0714'.
-14.00560224 + -2x + x2 = 0

Move the constant term to the right:

Add '14.00560224' to each side of the equation.
-14.00560224 + -2x + 14.00560224 + x2 = 0 + 14.00560224

Reorder the terms:
-14.00560224 + 14.00560224 + -2x + x2 = 0 + 14.00560224

Combine like terms: -14.00560224 + 14.00560224 = 0.00000000
0.00000000 + -2x + x2 = 0 + 14.00560224
-2x + x2 = 0 + 14.00560224

Combine like terms: 0 + 14.00560224 = 14.00560224
-2x + x2 = 14.00560224

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 14.00560224 + 1

Reorder the terms:
1 + -2x + x2 = 14.00560224 + 1

Combine like terms: 14.00560224 + 1 = 15.00560224
1 + -2x + x2 = 15.00560224

Factor a perfect square on the left side:
(x + -1)(x + -1) = 15.00560224

Calculate the square root of the right side: 3.873706525

Break this problem into two subproblems by setting 
(x + -1) equal to 3.873706525 and -3.873706525.

Subproblem 1
x + -1 = 3.873706525

Simplifying
x + -1 = 3.873706525

Reorder the terms:
-1 + x = 3.873706525

Solving
-1 + x = 3.873706525

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 3.873706525 + 1

Combine like terms: -1 + 1 = 0
0 + x = 3.873706525 + 1
x = 3.873706525 + 1

Combine like terms: 3.873706525 + 1 = 4.873706525
x = 4.873706525

Simplifying
x = 4.873706525

Subproblem 2
x + -1 = -3.873706525

Simplifying
x + -1 = -3.873706525

Reorder the terms:
-1 + x = -3.873706525

Solving
-1 + x = -3.873706525

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -3.873706525 + 1

Combine like terms: -1 + 1 = 0
0 + x = -3.873706525 + 1
x = -3.873706525 + 1

Combine like terms: -3.873706525 + 1 = -2.873706525
x = -2.873706525

Simplifying
x = -2.873706525

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.873706525, -2.873706525}