71x^2-119x+49=0

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Solution for 71x^2-119x+49=0 equation:


Simplifying
71x2 + -119x + 49 = 0

Reorder the terms:
49 + -119x + 71x2 = 0

Solving
49 + -119x + 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'.
0.6901408451 + -1.676056338x + x2 = 0

Move the constant term to the right:

Add '-0.6901408451' to each side of the equation.
0.6901408451 + -1.676056338x + -0.6901408451 + x2 = 0 + -0.6901408451

Reorder the terms:
0.6901408451 + -0.6901408451 + -1.676056338x + x2 = 0 + -0.6901408451

Combine like terms: 0.6901408451 + -0.6901408451 = 0.0000000000
0.0000000000 + -1.676056338x + x2 = 0 + -0.6901408451
-1.676056338x + x2 = 0 + -0.6901408451

Combine like terms: 0 + -0.6901408451 = -0.6901408451
-1.676056338x + x2 = -0.6901408451

The x term is -1.676056338x.  Take half its coefficient (-0.838028169).
Square it (0.7022912120) and add it to both sides.

Add '0.7022912120' to each side of the equation.
-1.676056338x + 0.7022912120 + x2 = -0.6901408451 + 0.7022912120

Reorder the terms:
0.7022912120 + -1.676056338x + x2 = -0.6901408451 + 0.7022912120

Combine like terms: -0.6901408451 + 0.7022912120 = 0.0121503669
0.7022912120 + -1.676056338x + x2 = 0.0121503669

Factor a perfect square on the left side:
(x + -0.838028169)(x + -0.838028169) = 0.0121503669

Calculate the square root of the right side: 0.110228703

Break this problem into two subproblems by setting 
(x + -0.838028169) equal to 0.110228703 and -0.110228703.

Subproblem 1

x + -0.838028169 = 0.110228703 Simplifying x + -0.838028169 = 0.110228703 Reorder the terms: -0.838028169 + x = 0.110228703 Solving -0.838028169 + x = 0.110228703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.838028169' to each side of the equation. -0.838028169 + 0.838028169 + x = 0.110228703 + 0.838028169 Combine like terms: -0.838028169 + 0.838028169 = 0.000000000 0.000000000 + x = 0.110228703 + 0.838028169 x = 0.110228703 + 0.838028169 Combine like terms: 0.110228703 + 0.838028169 = 0.948256872 x = 0.948256872 Simplifying x = 0.948256872

Subproblem 2

x + -0.838028169 = -0.110228703 Simplifying x + -0.838028169 = -0.110228703 Reorder the terms: -0.838028169 + x = -0.110228703 Solving -0.838028169 + x = -0.110228703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.838028169' to each side of the equation. -0.838028169 + 0.838028169 + x = -0.110228703 + 0.838028169 Combine like terms: -0.838028169 + 0.838028169 = 0.000000000 0.000000000 + x = -0.110228703 + 0.838028169 x = -0.110228703 + 0.838028169 Combine like terms: -0.110228703 + 0.838028169 = 0.727799466 x = 0.727799466 Simplifying x = 0.727799466

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.948256872, 0.727799466}

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