7x^2-16x+1=0

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Solution for 7x^2-16x+1=0 equation:


Simplifying
7x2 + -16x + 1 = 0

Reorder the terms:
1 + -16x + 7x2 = 0

Solving
1 + -16x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
0.1428571429 + -2.285714286x + x2 = 0

Move the constant term to the right:

Add '-0.1428571429' to each side of the equation.
0.1428571429 + -2.285714286x + -0.1428571429 + x2 = 0 + -0.1428571429

Reorder the terms:
0.1428571429 + -0.1428571429 + -2.285714286x + x2 = 0 + -0.1428571429

Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000
0.0000000000 + -2.285714286x + x2 = 0 + -0.1428571429
-2.285714286x + x2 = 0 + -0.1428571429

Combine like terms: 0 + -0.1428571429 = -0.1428571429
-2.285714286x + x2 = -0.1428571429

The x term is -2.285714286x.  Take half its coefficient (-1.142857143).
Square it (1.306122449) and add it to both sides.

Add '1.306122449' to each side of the equation.
-2.285714286x + 1.306122449 + x2 = -0.1428571429 + 1.306122449

Reorder the terms:
1.306122449 + -2.285714286x + x2 = -0.1428571429 + 1.306122449

Combine like terms: -0.1428571429 + 1.306122449 = 1.1632653061
1.306122449 + -2.285714286x + x2 = 1.1632653061

Factor a perfect square on the left side:
(x + -1.142857143)(x + -1.142857143) = 1.1632653061

Calculate the square root of the right side: 1.078547776

Break this problem into two subproblems by setting 
(x + -1.142857143) equal to 1.078547776 and -1.078547776.

Subproblem 1

x + -1.142857143 = 1.078547776 Simplifying x + -1.142857143 = 1.078547776 Reorder the terms: -1.142857143 + x = 1.078547776 Solving -1.142857143 + x = 1.078547776 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.142857143' to each side of the equation. -1.142857143 + 1.142857143 + x = 1.078547776 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + x = 1.078547776 + 1.142857143 x = 1.078547776 + 1.142857143 Combine like terms: 1.078547776 + 1.142857143 = 2.221404919 x = 2.221404919 Simplifying x = 2.221404919

Subproblem 2

x + -1.142857143 = -1.078547776 Simplifying x + -1.142857143 = -1.078547776 Reorder the terms: -1.142857143 + x = -1.078547776 Solving -1.142857143 + x = -1.078547776 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.142857143' to each side of the equation. -1.142857143 + 1.142857143 + x = -1.078547776 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + x = -1.078547776 + 1.142857143 x = -1.078547776 + 1.142857143 Combine like terms: -1.078547776 + 1.142857143 = 0.064309367 x = 0.064309367 Simplifying x = 0.064309367

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.221404919, 0.064309367}

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