3x^2-123x+10=0

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Solution for 3x^2-123x+10=0 equation:


Simplifying
3x2 + -123x + 10 = 0

Reorder the terms:
10 + -123x + 3x2 = 0

Solving
10 + -123x + 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'.
3.333333333 + -41x + x2 = 0

Move the constant term to the right:

Add '-3.333333333' to each side of the equation.
3.333333333 + -41x + -3.333333333 + x2 = 0 + -3.333333333

Reorder the terms:
3.333333333 + -3.333333333 + -41x + x2 = 0 + -3.333333333

Combine like terms: 3.333333333 + -3.333333333 = 0.000000000
0.000000000 + -41x + x2 = 0 + -3.333333333
-41x + x2 = 0 + -3.333333333

Combine like terms: 0 + -3.333333333 = -3.333333333
-41x + x2 = -3.333333333

The x term is -41x.  Take half its coefficient (-20.5).
Square it (420.25) and add it to both sides.

Add '420.25' to each side of the equation.
-41x + 420.25 + x2 = -3.333333333 + 420.25

Reorder the terms:
420.25 + -41x + x2 = -3.333333333 + 420.25

Combine like terms: -3.333333333 + 420.25 = 416.916666667
420.25 + -41x + x2 = 416.916666667

Factor a perfect square on the left side:
(x + -20.5)(x + -20.5) = 416.916666667

Calculate the square root of the right side: 20.418537329

Break this problem into two subproblems by setting 
(x + -20.5) equal to 20.418537329 and -20.418537329.

Subproblem 1

x + -20.5 = 20.418537329 Simplifying x + -20.5 = 20.418537329 Reorder the terms: -20.5 + x = 20.418537329 Solving -20.5 + x = 20.418537329 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20.5' to each side of the equation. -20.5 + 20.5 + x = 20.418537329 + 20.5 Combine like terms: -20.5 + 20.5 = 0.0 0.0 + x = 20.418537329 + 20.5 x = 20.418537329 + 20.5 Combine like terms: 20.418537329 + 20.5 = 40.918537329 x = 40.918537329 Simplifying x = 40.918537329

Subproblem 2

x + -20.5 = -20.418537329 Simplifying x + -20.5 = -20.418537329 Reorder the terms: -20.5 + x = -20.418537329 Solving -20.5 + x = -20.418537329 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20.5' to each side of the equation. -20.5 + 20.5 + x = -20.418537329 + 20.5 Combine like terms: -20.5 + 20.5 = 0.0 0.0 + x = -20.418537329 + 20.5 x = -20.418537329 + 20.5 Combine like terms: -20.418537329 + 20.5 = 0.081462671 x = 0.081462671 Simplifying x = 0.081462671

Solution

The solution to the problem is based on the solutions from the subproblems. x = {40.918537329, 0.081462671}

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