3x^2-35x+7=0

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Solution for 3x^2-35x+7=0 equation:


Simplifying
3x2 + -35x + 7 = 0

Reorder the terms:
7 + -35x + 3x2 = 0

Solving
7 + -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'.
2.333333333 + -11.66666667x + x2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + -11.66666667x + -2.333333333 + x2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + -11.66666667x + x2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + -11.66666667x + x2 = 0 + -2.333333333
-11.66666667x + x2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
-11.66666667x + x2 = -2.333333333

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 = -2.333333333 + 34.02777780

Reorder the terms:
34.02777780 + -11.66666667x + x2 = -2.333333333 + 34.02777780

Combine like terms: -2.333333333 + 34.02777780 = 31.694444467
34.02777780 + -11.66666667x + x2 = 31.694444467

Factor a perfect square on the left side:
(x + -5.833333335)(x + -5.833333335) = 31.694444467

Calculate the square root of the right side: 5.62978192

Break this problem into two subproblems by setting 
(x + -5.833333335) equal to 5.62978192 and -5.62978192.


Subproblem 1
x + -5.833333335 = 5.62978192

Simplifying
x + -5.833333335 = 5.62978192

Reorder the terms:
-5.833333335 + x = 5.62978192

Solving
-5.833333335 + x = 5.62978192

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 = 5.62978192 + 5.833333335

Combine like terms: -5.833333335 + 5.833333335 = 0.000000000
0.000000000 + x = 5.62978192 + 5.833333335
x = 5.62978192 + 5.833333335

Combine like terms: 5.62978192 + 5.833333335 = 11.463115255
x = 11.463115255

Simplifying
x = 11.463115255


Subproblem 2
x + -5.833333335 = -5.62978192

Simplifying
x + -5.833333335 = -5.62978192

Reorder the terms:
-5.833333335 + x = -5.62978192

Solving
-5.833333335 + x = -5.62978192

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 = -5.62978192 + 5.833333335

Combine like terms: -5.833333335 + 5.833333335 = 0.000000000
0.000000000 + x = -5.62978192 + 5.833333335
x = -5.62978192 + 5.833333335

Combine like terms: -5.62978192 + 5.833333335 = 0.203551415
x = 0.203551415

Simplifying
x = 0.203551415


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.463115255, 0.203551415}

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