3x^2-35x+76=0

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Solution for 3x^2-35x+76=0 equation: 


Simplifying
3x2 + -35x + 76 = 0

Reorder the terms:
76 + -35x + 3x2 = 0

Solving
76 + -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'.
25.33333333 + -11.66666667x + x2 = 0

Move the constant term to the right:

Add '-25.33333333' to each side of the equation.
25.33333333 + -11.66666667x + -25.33333333 + x2 = 0 + -25.33333333

Reorder the terms:
25.33333333 + -25.33333333 + -11.66666667x + x2 = 0 + -25.33333333

Combine like terms: 25.33333333 + -25.33333333 = 0.00000000
0.00000000 + -11.66666667x + x2 = 0 + -25.33333333
-11.66666667x + x2 = 0 + -25.33333333

Combine like terms: 0 + -25.33333333 = -25.33333333
-11.66666667x + x2 = -25.33333333

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 = -25.33333333 + 34.02777780

Reorder the terms:
34.02777780 + -11.66666667x + x2 = -25.33333333 + 34.02777780

Combine like terms: -25.33333333 + 34.02777780 = 8.69444447
34.02777780 + -11.66666667x + x2 = 8.69444447

Factor a perfect square on the left side:
(x + -5.833333335)(x + -5.833333335) = 8.69444447

Calculate the square root of the right side: 2.94863434

Break this problem into two subproblems by setting 
(x + -5.833333335) equal to 2.94863434 and -2.94863434.


Subproblem 1
x + -5.833333335 = 2.94863434

Simplifying
x + -5.833333335 = 2.94863434

Reorder the terms:
-5.833333335 + x = 2.94863434

Solving
-5.833333335 + x = 2.94863434

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 = 2.94863434 + 5.833333335

Combine like terms: -5.833333335 + 5.833333335 = 0.000000000
0.000000000 + x = 2.94863434 + 5.833333335
x = 2.94863434 + 5.833333335

Combine like terms: 2.94863434 + 5.833333335 = 8.781967675
x = 8.781967675

Simplifying
x = 8.781967675


Subproblem 2
x + -5.833333335 = -2.94863434

Simplifying
x + -5.833333335 = -2.94863434

Reorder the terms:
-5.833333335 + x = -2.94863434

Solving
-5.833333335 + x = -2.94863434

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 = -2.94863434 + 5.833333335

Combine like terms: -5.833333335 + 5.833333335 = 0.000000000
0.000000000 + x = -2.94863434 + 5.833333335
x = -2.94863434 + 5.833333335

Combine like terms: -2.94863434 + 5.833333335 = 2.884698995
x = 2.884698995

Simplifying
x = 2.884698995


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.781967675, 2.884698995}

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