16x^2-12x+1=0

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Solution for 16x^2-12x+1=0 equation:


Simplifying
16x2 + -12x + 1 = 0

Reorder the terms:
1 + -12x + 16x2 = 0

Solving
1 + -12x + 16x2 = 0

Solving for variable 'x'.

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

Divide each side by '16'.
0.0625 + -0.75x + x2 = 0

Move the constant term to the right:

Add '-0.0625' to each side of the equation.
0.0625 + -0.75x + -0.0625 + x2 = 0 + -0.0625

Reorder the terms:
0.0625 + -0.0625 + -0.75x + x2 = 0 + -0.0625

Combine like terms: 0.0625 + -0.0625 = 0.0000
0.0000 + -0.75x + x2 = 0 + -0.0625
-0.75x + x2 = 0 + -0.0625

Combine like terms: 0 + -0.0625 = -0.0625
-0.75x + x2 = -0.0625

The x term is -0.75x.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75x + 0.140625 + x2 = -0.0625 + 0.140625

Reorder the terms:
0.140625 + -0.75x + x2 = -0.0625 + 0.140625

Combine like terms: -0.0625 + 0.140625 = 0.078125
0.140625 + -0.75x + x2 = 0.078125

Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = 0.078125

Calculate the square root of the right side: 0.279508497

Break this problem into two subproblems by setting 
(x + -0.375) equal to 0.279508497 and -0.279508497.

Subproblem 1

x + -0.375 = 0.279508497 Simplifying x + -0.375 = 0.279508497 Reorder the terms: -0.375 + x = 0.279508497 Solving -0.375 + x = 0.279508497 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 0.279508497 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 0.279508497 + 0.375 x = 0.279508497 + 0.375 Combine like terms: 0.279508497 + 0.375 = 0.654508497 x = 0.654508497 Simplifying x = 0.654508497

Subproblem 2

x + -0.375 = -0.279508497 Simplifying x + -0.375 = -0.279508497 Reorder the terms: -0.375 + x = -0.279508497 Solving -0.375 + x = -0.279508497 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -0.279508497 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -0.279508497 + 0.375 x = -0.279508497 + 0.375 Combine like terms: -0.279508497 + 0.375 = 0.095491503 x = 0.095491503 Simplifying x = 0.095491503

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.654508497, 0.095491503}

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