7x^2-12x+1=0

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Solution for 7x^2-12x+1=0 equation:


Simplifying
7x2 + -12x + 1 = 0

Reorder the terms:
1 + -12x + 7x2 = 0

Solving
1 + -12x + 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 + -1.714285714x + x2 = 0

Move the constant term to the right:

Add '-0.1428571429' to each side of the equation.
0.1428571429 + -1.714285714x + -0.1428571429 + x2 = 0 + -0.1428571429

Reorder the terms:
0.1428571429 + -0.1428571429 + -1.714285714x + x2 = 0 + -0.1428571429

Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000
0.0000000000 + -1.714285714x + x2 = 0 + -0.1428571429
-1.714285714x + x2 = 0 + -0.1428571429

Combine like terms: 0 + -0.1428571429 = -0.1428571429
-1.714285714x + x2 = -0.1428571429

The x term is -1.714285714x.  Take half its coefficient (-0.857142857).
Square it (0.7346938773) and add it to both sides.

Add '0.7346938773' to each side of the equation.
-1.714285714x + 0.7346938773 + x2 = -0.1428571429 + 0.7346938773

Reorder the terms:
0.7346938773 + -1.714285714x + x2 = -0.1428571429 + 0.7346938773

Combine like terms: -0.1428571429 + 0.7346938773 = 0.5918367344
0.7346938773 + -1.714285714x + x2 = 0.5918367344

Factor a perfect square on the left side:
(x + -0.857142857)(x + -0.857142857) = 0.5918367344

Calculate the square root of the right side: 0.769309258

Break this problem into two subproblems by setting 
(x + -0.857142857) equal to 0.769309258 and -0.769309258.

Subproblem 1

x + -0.857142857 = 0.769309258 Simplifying x + -0.857142857 = 0.769309258 Reorder the terms: -0.857142857 + x = 0.769309258 Solving -0.857142857 + x = 0.769309258 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.857142857' to each side of the equation. -0.857142857 + 0.857142857 + x = 0.769309258 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + x = 0.769309258 + 0.857142857 x = 0.769309258 + 0.857142857 Combine like terms: 0.769309258 + 0.857142857 = 1.626452115 x = 1.626452115 Simplifying x = 1.626452115

Subproblem 2

x + -0.857142857 = -0.769309258 Simplifying x + -0.857142857 = -0.769309258 Reorder the terms: -0.857142857 + x = -0.769309258 Solving -0.857142857 + x = -0.769309258 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.857142857' to each side of the equation. -0.857142857 + 0.857142857 + x = -0.769309258 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + x = -0.769309258 + 0.857142857 x = -0.769309258 + 0.857142857 Combine like terms: -0.769309258 + 0.857142857 = 0.087833599 x = 0.087833599 Simplifying x = 0.087833599

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.626452115, 0.087833599}

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