28x^2+2x-1=0

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Solution for 28x^2+2x-1=0 equation: 


Simplifying
28x2 + 2x + -1 = 0

Reorder the terms:
-1 + 2x + 28x2 = 0

Solving
-1 + 2x + 28x2 = 0

Solving for variable 'x'.

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

Divide each side by '28'.
-0.03571428571 + 0.07142857143x + x2 = 0

Move the constant term to the right:

Add '0.03571428571' to each side of the equation.
-0.03571428571 + 0.07142857143x + 0.03571428571 + x2 = 0 + 0.03571428571

Reorder the terms:
-0.03571428571 + 0.03571428571 + 0.07142857143x + x2 = 0 + 0.03571428571

Combine like terms: -0.03571428571 + 0.03571428571 = 0.00000000000
0.00000000000 + 0.07142857143x + x2 = 0 + 0.03571428571
0.07142857143x + x2 = 0 + 0.03571428571

Combine like terms: 0 + 0.03571428571 = 0.03571428571
0.07142857143x + x2 = 0.03571428571

The x term is 0.07142857143x.  Take half its coefficient (0.03571428572).
Square it (0.001275510204) and add it to both sides.

Add '0.001275510204' to each side of the equation.
0.07142857143x + 0.001275510204 + x2 = 0.03571428571 + 0.001275510204

Reorder the terms:
0.001275510204 + 0.07142857143x + x2 = 0.03571428571 + 0.001275510204

Combine like terms: 0.03571428571 + 0.001275510204 = 0.036989795914
0.001275510204 + 0.07142857143x + x2 = 0.036989795914

Factor a perfect square on the left side:
(x + 0.03571428572)(x + 0.03571428572) = 0.036989795914

Calculate the square root of the right side: 0.192327315

Break this problem into two subproblems by setting 
(x + 0.03571428572) equal to 0.192327315 and -0.192327315.


Subproblem 1
x + 0.03571428572 = 0.192327315

Simplifying
x + 0.03571428572 = 0.192327315

Reorder the terms:
0.03571428572 + x = 0.192327315

Solving
0.03571428572 + x = 0.192327315

Solving for variable 'x'.

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

Add '-0.03571428572' to each side of the equation.
0.03571428572 + -0.03571428572 + x = 0.192327315 + -0.03571428572

Combine like terms: 0.03571428572 + -0.03571428572 = 0.00000000000
0.00000000000 + x = 0.192327315 + -0.03571428572
x = 0.192327315 + -0.03571428572

Combine like terms: 0.192327315 + -0.03571428572 = 0.15661302928
x = 0.15661302928

Simplifying
x = 0.15661302928


Subproblem 2
x + 0.03571428572 = -0.192327315

Simplifying
x + 0.03571428572 = -0.192327315

Reorder the terms:
0.03571428572 + x = -0.192327315

Solving
0.03571428572 + x = -0.192327315

Solving for variable 'x'.

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

Add '-0.03571428572' to each side of the equation.
0.03571428572 + -0.03571428572 + x = -0.192327315 + -0.03571428572

Combine like terms: 0.03571428572 + -0.03571428572 = 0.00000000000
0.00000000000 + x = -0.192327315 + -0.03571428572
x = -0.192327315 + -0.03571428572

Combine like terms: -0.192327315 + -0.03571428572 = -0.22804160072
x = -0.22804160072

Simplifying
x = -0.22804160072


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.15661302928, -0.22804160072}

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