3x^2-82x+418=0

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Solution for 3x^2-82x+418=0 equation:


Simplifying
3x2 + -82x + 418 = 0

Reorder the terms:
418 + -82x + 3x2 = 0

Solving
418 + -82x + 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'.
139.3333333 + -27.33333333x + x2 = 0

Move the constant term to the right:

Add '-139.3333333' to each side of the equation.
139.3333333 + -27.33333333x + -139.3333333 + x2 = 0 + -139.3333333

Reorder the terms:
139.3333333 + -139.3333333 + -27.33333333x + x2 = 0 + -139.3333333

Combine like terms: 139.3333333 + -139.3333333 = 0.0000000
0.0000000 + -27.33333333x + x2 = 0 + -139.3333333
-27.33333333x + x2 = 0 + -139.3333333

Combine like terms: 0 + -139.3333333 = -139.3333333
-27.33333333x + x2 = -139.3333333

The x term is -27.33333333x.  Take half its coefficient (-13.66666667).
Square it (186.7777779) and add it to both sides.

Add '186.7777779' to each side of the equation.
-27.33333333x + 186.7777779 + x2 = -139.3333333 + 186.7777779

Reorder the terms:
186.7777779 + -27.33333333x + x2 = -139.3333333 + 186.7777779

Combine like terms: -139.3333333 + 186.7777779 = 47.4444446
186.7777779 + -27.33333333x + x2 = 47.4444446

Factor a perfect square on the left side:
(x + -13.66666667)(x + -13.66666667) = 47.4444446

Calculate the square root of the right side: 6.887992785

Break this problem into two subproblems by setting 
(x + -13.66666667) equal to 6.887992785 and -6.887992785.

Subproblem 1

x + -13.66666667 = 6.887992785 Simplifying x + -13.66666667 = 6.887992785 Reorder the terms: -13.66666667 + x = 6.887992785 Solving -13.66666667 + x = 6.887992785 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.66666667' to each side of the equation. -13.66666667 + 13.66666667 + x = 6.887992785 + 13.66666667 Combine like terms: -13.66666667 + 13.66666667 = 0.00000000 0.00000000 + x = 6.887992785 + 13.66666667 x = 6.887992785 + 13.66666667 Combine like terms: 6.887992785 + 13.66666667 = 20.554659455 x = 20.554659455 Simplifying x = 20.554659455

Subproblem 2

x + -13.66666667 = -6.887992785 Simplifying x + -13.66666667 = -6.887992785 Reorder the terms: -13.66666667 + x = -6.887992785 Solving -13.66666667 + x = -6.887992785 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.66666667' to each side of the equation. -13.66666667 + 13.66666667 + x = -6.887992785 + 13.66666667 Combine like terms: -13.66666667 + 13.66666667 = 0.00000000 0.00000000 + x = -6.887992785 + 13.66666667 x = -6.887992785 + 13.66666667 Combine like terms: -6.887992785 + 13.66666667 = 6.778673885 x = 6.778673885 Simplifying x = 6.778673885

Solution

The solution to the problem is based on the solutions from the subproblems. x = {20.554659455, 6.778673885}

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