28x^2-7x-1=0

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Solution for 28x^2-7x-1=0 equation: 


Simplifying
28x2 + -7x + -1 = 0

Reorder the terms:
-1 + -7x + 28x2 = 0

Solving
-1 + -7x + 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 + -0.25x + x2 = 0

Move the constant term to the right:

Add '0.03571428571' to each side of the equation.
-0.03571428571 + -0.25x + 0.03571428571 + x2 = 0 + 0.03571428571

Reorder the terms:
-0.03571428571 + 0.03571428571 + -0.25x + x2 = 0 + 0.03571428571

Combine like terms: -0.03571428571 + 0.03571428571 = 0.00000000000
0.00000000000 + -0.25x + x2 = 0 + 0.03571428571
-0.25x + x2 = 0 + 0.03571428571

Combine like terms: 0 + 0.03571428571 = 0.03571428571
-0.25x + x2 = 0.03571428571

The x term is -0.25x.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25x + 0.015625 + x2 = 0.03571428571 + 0.015625

Reorder the terms:
0.015625 + -0.25x + x2 = 0.03571428571 + 0.015625

Combine like terms: 0.03571428571 + 0.015625 = 0.05133928571
0.015625 + -0.25x + x2 = 0.05133928571

Factor a perfect square on the left side:
(x + -0.125)(x + -0.125) = 0.05133928571

Calculate the square root of the right side: 0.226581742

Break this problem into two subproblems by setting 
(x + -0.125) equal to 0.226581742 and -0.226581742.


Subproblem 1
x + -0.125 = 0.226581742

Simplifying
x + -0.125 = 0.226581742

Reorder the terms:
-0.125 + x = 0.226581742

Solving
-0.125 + x = 0.226581742

Solving for variable 'x'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + x = 0.226581742 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = 0.226581742 + 0.125
x = 0.226581742 + 0.125

Combine like terms: 0.226581742 + 0.125 = 0.351581742
x = 0.351581742

Simplifying
x = 0.351581742


Subproblem 2
x + -0.125 = -0.226581742

Simplifying
x + -0.125 = -0.226581742

Reorder the terms:
-0.125 + x = -0.226581742

Solving
-0.125 + x = -0.226581742

Solving for variable 'x'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + x = -0.226581742 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = -0.226581742 + 0.125
x = -0.226581742 + 0.125

Combine like terms: -0.226581742 + 0.125 = -0.101581742
x = -0.101581742

Simplifying
x = -0.101581742


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.351581742, -0.101581742}

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