8x^2-x=1

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Solution for 8x^2-x=1 equation:


Simplifying
8x2 + -1x = 1

Reorder the terms:
-1x + 8x2 = 1

Solving
-1x + 8x2 = 1

Solving for variable 'x'.

Reorder the terms:
-1 + -1x + 8x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + -1x + 8x2 = 0

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

Divide each side by '8'.
-0.125 + -0.125x + x2 = 0

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + -0.125x + 0.125 + x2 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + -0.125x + x2 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + -0.125x + x2 = 0 + 0.125
-0.125x + x2 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
-0.125x + x2 = 0.125

The x term is -0.125x.  Take half its coefficient (-0.0625).
Square it (0.00390625) and add it to both sides.

Add '0.00390625' to each side of the equation.
-0.125x + 0.00390625 + x2 = 0.125 + 0.00390625

Reorder the terms:
0.00390625 + -0.125x + x2 = 0.125 + 0.00390625

Combine like terms: 0.125 + 0.00390625 = 0.12890625
0.00390625 + -0.125x + x2 = 0.12890625

Factor a perfect square on the left side:
(x + -0.0625)(x + -0.0625) = 0.12890625

Calculate the square root of the right side: 0.359035165

Break this problem into two subproblems by setting 
(x + -0.0625) equal to 0.359035165 and -0.359035165.

Subproblem 1

x + -0.0625 = 0.359035165 Simplifying x + -0.0625 = 0.359035165 Reorder the terms: -0.0625 + x = 0.359035165 Solving -0.0625 + x = 0.359035165 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = 0.359035165 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = 0.359035165 + 0.0625 x = 0.359035165 + 0.0625 Combine like terms: 0.359035165 + 0.0625 = 0.421535165 x = 0.421535165 Simplifying x = 0.421535165

Subproblem 2

x + -0.0625 = -0.359035165 Simplifying x + -0.0625 = -0.359035165 Reorder the terms: -0.0625 + x = -0.359035165 Solving -0.0625 + x = -0.359035165 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = -0.359035165 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = -0.359035165 + 0.0625 x = -0.359035165 + 0.0625 Combine like terms: -0.359035165 + 0.0625 = -0.296535165 x = -0.296535165 Simplifying x = -0.296535165

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.421535165, -0.296535165}

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