7x^2-32x+1=0

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Solution for 7x^2-32x+1=0 equation:


Simplifying
7x2 + -32x + 1 = 0

Reorder the terms:
1 + -32x + 7x2 = 0

Solving
1 + -32x + 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 + -4.571428571x + x2 = 0

Move the constant term to the right:

Add '-0.1428571429' to each side of the equation.
0.1428571429 + -4.571428571x + -0.1428571429 + x2 = 0 + -0.1428571429

Reorder the terms:
0.1428571429 + -0.1428571429 + -4.571428571x + x2 = 0 + -0.1428571429

Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000
0.0000000000 + -4.571428571x + x2 = 0 + -0.1428571429
-4.571428571x + x2 = 0 + -0.1428571429

Combine like terms: 0 + -0.1428571429 = -0.1428571429
-4.571428571x + x2 = -0.1428571429

The x term is -4.571428571x.  Take half its coefficient (-2.285714286).
Square it (5.224489797) and add it to both sides.

Add '5.224489797' to each side of the equation.
-4.571428571x + 5.224489797 + x2 = -0.1428571429 + 5.224489797

Reorder the terms:
5.224489797 + -4.571428571x + x2 = -0.1428571429 + 5.224489797

Combine like terms: -0.1428571429 + 5.224489797 = 5.0816326541
5.224489797 + -4.571428571x + x2 = 5.0816326541

Factor a perfect square on the left side:
(x + -2.285714286)(x + -2.285714286) = 5.0816326541

Calculate the square root of the right side: 2.254247691

Break this problem into two subproblems by setting 
(x + -2.285714286) equal to 2.254247691 and -2.254247691.

Subproblem 1

x + -2.285714286 = 2.254247691 Simplifying x + -2.285714286 = 2.254247691 Reorder the terms: -2.285714286 + x = 2.254247691 Solving -2.285714286 + x = 2.254247691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.285714286' to each side of the equation. -2.285714286 + 2.285714286 + x = 2.254247691 + 2.285714286 Combine like terms: -2.285714286 + 2.285714286 = 0.000000000 0.000000000 + x = 2.254247691 + 2.285714286 x = 2.254247691 + 2.285714286 Combine like terms: 2.254247691 + 2.285714286 = 4.539961977 x = 4.539961977 Simplifying x = 4.539961977

Subproblem 2

x + -2.285714286 = -2.254247691 Simplifying x + -2.285714286 = -2.254247691 Reorder the terms: -2.285714286 + x = -2.254247691 Solving -2.285714286 + x = -2.254247691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.285714286' to each side of the equation. -2.285714286 + 2.285714286 + x = -2.254247691 + 2.285714286 Combine like terms: -2.285714286 + 2.285714286 = 0.000000000 0.000000000 + x = -2.254247691 + 2.285714286 x = -2.254247691 + 2.285714286 Combine like terms: -2.254247691 + 2.285714286 = 0.031466595 x = 0.031466595 Simplifying x = 0.031466595

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.539961977, 0.031466595}

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