71x^2-57x+2=0

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Solution for 71x^2-57x+2=0 equation:


Simplifying
71x2 + -57x + 2 = 0

Reorder the terms:
2 + -57x + 71x2 = 0

Solving
2 + -57x + 71x2 = 0

Solving for variable 'x'.

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

Divide each side by '71'.
0.02816901408 + -0.8028169014x + x2 = 0

Move the constant term to the right:

Add '-0.02816901408' to each side of the equation.
0.02816901408 + -0.8028169014x + -0.02816901408 + x2 = 0 + -0.02816901408

Reorder the terms:
0.02816901408 + -0.02816901408 + -0.8028169014x + x2 = 0 + -0.02816901408

Combine like terms: 0.02816901408 + -0.02816901408 = 0.00000000000
0.00000000000 + -0.8028169014x + x2 = 0 + -0.02816901408
-0.8028169014x + x2 = 0 + -0.02816901408

Combine like terms: 0 + -0.02816901408 = -0.02816901408
-0.8028169014x + x2 = -0.02816901408

The x term is -0.8028169014x.  Take half its coefficient (-0.4014084507).
Square it (0.1611287443) and add it to both sides.

Add '0.1611287443' to each side of the equation.
-0.8028169014x + 0.1611287443 + x2 = -0.02816901408 + 0.1611287443

Reorder the terms:
0.1611287443 + -0.8028169014x + x2 = -0.02816901408 + 0.1611287443

Combine like terms: -0.02816901408 + 0.1611287443 = 0.13295973022
0.1611287443 + -0.8028169014x + x2 = 0.13295973022

Factor a perfect square on the left side:
(x + -0.4014084507)(x + -0.4014084507) = 0.13295973022

Calculate the square root of the right side: 0.364636436

Break this problem into two subproblems by setting 
(x + -0.4014084507) equal to 0.364636436 and -0.364636436.

Subproblem 1

x + -0.4014084507 = 0.364636436 Simplifying x + -0.4014084507 = 0.364636436 Reorder the terms: -0.4014084507 + x = 0.364636436 Solving -0.4014084507 + x = 0.364636436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4014084507' to each side of the equation. -0.4014084507 + 0.4014084507 + x = 0.364636436 + 0.4014084507 Combine like terms: -0.4014084507 + 0.4014084507 = 0.0000000000 0.0000000000 + x = 0.364636436 + 0.4014084507 x = 0.364636436 + 0.4014084507 Combine like terms: 0.364636436 + 0.4014084507 = 0.7660448867 x = 0.7660448867 Simplifying x = 0.7660448867

Subproblem 2

x + -0.4014084507 = -0.364636436 Simplifying x + -0.4014084507 = -0.364636436 Reorder the terms: -0.4014084507 + x = -0.364636436 Solving -0.4014084507 + x = -0.364636436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4014084507' to each side of the equation. -0.4014084507 + 0.4014084507 + x = -0.364636436 + 0.4014084507 Combine like terms: -0.4014084507 + 0.4014084507 = 0.0000000000 0.0000000000 + x = -0.364636436 + 0.4014084507 x = -0.364636436 + 0.4014084507 Combine like terms: -0.364636436 + 0.4014084507 = 0.0367720147 x = 0.0367720147 Simplifying x = 0.0367720147

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.7660448867, 0.0367720147}

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