3x^2-41x+102=0

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Solution for 3x^2-41x+102=0 equation:


Simplifying
3x2 + -41x + 102 = 0

Reorder the terms:
102 + -41x + 3x2 = 0

Solving
102 + -41x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
34 + -13.66666667x + x2 = 0

Move the constant term to the right:

Add '-34' to each side of the equation.
34 + -13.66666667x + -34 + x2 = 0 + -34

Reorder the terms:
34 + -34 + -13.66666667x + x2 = 0 + -34

Combine like terms: 34 + -34 = 0
0 + -13.66666667x + x2 = 0 + -34
-13.66666667x + x2 = 0 + -34

Combine like terms: 0 + -34 = -34
-13.66666667x + x2 = -34

The x term is -13.66666667x.  Take half its coefficient (-6.833333335).
Square it (46.69444447) and add it to both sides.

Add '46.69444447' to each side of the equation.
-13.66666667x + 46.69444447 + x2 = -34 + 46.69444447

Reorder the terms:
46.69444447 + -13.66666667x + x2 = -34 + 46.69444447

Combine like terms: -34 + 46.69444447 = 12.69444447
46.69444447 + -13.66666667x + x2 = 12.69444447

Factor a perfect square on the left side:
(x + -6.833333335)(x + -6.833333335) = 12.69444447

Calculate the square root of the right side: 3.562926391

Break this problem into two subproblems by setting 
(x + -6.833333335) equal to 3.562926391 and -3.562926391.

Subproblem 1

x + -6.833333335 = 3.562926391 Simplifying x + -6.833333335 = 3.562926391 Reorder the terms: -6.833333335 + x = 3.562926391 Solving -6.833333335 + x = 3.562926391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.833333335' to each side of the equation. -6.833333335 + 6.833333335 + x = 3.562926391 + 6.833333335 Combine like terms: -6.833333335 + 6.833333335 = 0.000000000 0.000000000 + x = 3.562926391 + 6.833333335 x = 3.562926391 + 6.833333335 Combine like terms: 3.562926391 + 6.833333335 = 10.396259726 x = 10.396259726 Simplifying x = 10.396259726

Subproblem 2

x + -6.833333335 = -3.562926391 Simplifying x + -6.833333335 = -3.562926391 Reorder the terms: -6.833333335 + x = -3.562926391 Solving -6.833333335 + x = -3.562926391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.833333335' to each side of the equation. -6.833333335 + 6.833333335 + x = -3.562926391 + 6.833333335 Combine like terms: -6.833333335 + 6.833333335 = 0.000000000 0.000000000 + x = -3.562926391 + 6.833333335 x = -3.562926391 + 6.833333335 Combine like terms: -3.562926391 + 6.833333335 = 3.270406944 x = 3.270406944 Simplifying x = 3.270406944

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.396259726, 3.270406944}

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