3x^2-35x+74=0

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Solution for 3x^2-35x+74=0 equation: 


Simplifying
3x2 + -35x + 74 = 0

Reorder the terms:
74 + -35x + 3x2 = 0

Solving
74 + -35x + 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'.
24.66666667 + -11.66666667x + x2 = 0

Move the constant term to the right:

Add '-24.66666667' to each side of the equation.
24.66666667 + -11.66666667x + -24.66666667 + x2 = 0 + -24.66666667

Reorder the terms:
24.66666667 + -24.66666667 + -11.66666667x + x2 = 0 + -24.66666667

Combine like terms: 24.66666667 + -24.66666667 = 0.00000000
0.00000000 + -11.66666667x + x2 = 0 + -24.66666667
-11.66666667x + x2 = 0 + -24.66666667

Combine like terms: 0 + -24.66666667 = -24.66666667
-11.66666667x + x2 = -24.66666667

The x term is -11.66666667x.  Take half its coefficient (-5.833333335).
Square it (34.02777780) and add it to both sides.

Add '34.02777780' to each side of the equation.
-11.66666667x + 34.02777780 + x2 = -24.66666667 + 34.02777780

Reorder the terms:
34.02777780 + -11.66666667x + x2 = -24.66666667 + 34.02777780

Combine like terms: -24.66666667 + 34.02777780 = 9.36111113
34.02777780 + -11.66666667x + x2 = 9.36111113

Factor a perfect square on the left side:
(x + -5.833333335)(x + -5.833333335) = 9.36111113

Calculate the square root of the right side: 3.059593295

Break this problem into two subproblems by setting 
(x + -5.833333335) equal to 3.059593295 and -3.059593295.


Subproblem 1
x + -5.833333335 = 3.059593295

Simplifying
x + -5.833333335 = 3.059593295

Reorder the terms:
-5.833333335 + x = 3.059593295

Solving
-5.833333335 + x = 3.059593295

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '5.833333335' to each side of the equation.
-5.833333335 + 5.833333335 + x = 3.059593295 + 5.833333335

Combine like terms: -5.833333335 + 5.833333335 = 0.000000000
0.000000000 + x = 3.059593295 + 5.833333335
x = 3.059593295 + 5.833333335

Combine like terms: 3.059593295 + 5.833333335 = 8.89292663
x = 8.89292663

Simplifying
x = 8.89292663


Subproblem 2
x + -5.833333335 = -3.059593295

Simplifying
x + -5.833333335 = -3.059593295

Reorder the terms:
-5.833333335 + x = -3.059593295

Solving
-5.833333335 + x = -3.059593295

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '5.833333335' to each side of the equation.
-5.833333335 + 5.833333335 + x = -3.059593295 + 5.833333335

Combine like terms: -5.833333335 + 5.833333335 = 0.000000000
0.000000000 + x = -3.059593295 + 5.833333335
x = -3.059593295 + 5.833333335

Combine like terms: -3.059593295 + 5.833333335 = 2.77374004
x = 2.77374004

Simplifying
x = 2.77374004


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.89292663, 2.77374004}

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