32x^2-16x+1=0

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Solution for 32x^2-16x+1=0 equation:


Simplifying
32x2 + -16x + 1 = 0

Reorder the terms:
1 + -16x + 32x2 = 0

Solving
1 + -16x + 32x2 = 0

Solving for variable 'x'.

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

Divide each side by '32'.
0.03125 + -0.5x + x2 = 0

Move the constant term to the right:

Add '-0.03125' to each side of the equation.
0.03125 + -0.5x + -0.03125 + x2 = 0 + -0.03125

Reorder the terms:
0.03125 + -0.03125 + -0.5x + x2 = 0 + -0.03125

Combine like terms: 0.03125 + -0.03125 = 0.00000
0.00000 + -0.5x + x2 = 0 + -0.03125
-0.5x + x2 = 0 + -0.03125

Combine like terms: 0 + -0.03125 = -0.03125
-0.5x + x2 = -0.03125

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = -0.03125 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = -0.03125 + 0.0625

Combine like terms: -0.03125 + 0.0625 = 0.03125
0.0625 + -0.5x + x2 = 0.03125

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 0.03125

Calculate the square root of the right side: 0.176776695

Break this problem into two subproblems by setting 
(x + -0.25) equal to 0.176776695 and -0.176776695.

Subproblem 1

x + -0.25 = 0.176776695 Simplifying x + -0.25 = 0.176776695 Reorder the terms: -0.25 + x = 0.176776695 Solving -0.25 + x = 0.176776695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 0.176776695 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 0.176776695 + 0.25 x = 0.176776695 + 0.25 Combine like terms: 0.176776695 + 0.25 = 0.426776695 x = 0.426776695 Simplifying x = 0.426776695

Subproblem 2

x + -0.25 = -0.176776695 Simplifying x + -0.25 = -0.176776695 Reorder the terms: -0.25 + x = -0.176776695 Solving -0.25 + x = -0.176776695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -0.176776695 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -0.176776695 + 0.25 x = -0.176776695 + 0.25 Combine like terms: -0.176776695 + 0.25 = 0.073223305 x = 0.073223305 Simplifying x = 0.073223305

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.426776695, 0.073223305}

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