6x^2+5x-9=35

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Solution for 6x^2+5x-9=35 equation: 


Simplifying
6x2 + 5x + -9 = 35

Reorder the terms:
-9 + 5x + 6x2 = 35

Solving
-9 + 5x + 6x2 = 35

Solving for variable 'x'.

Reorder the terms:
-9 + -35 + 5x + 6x2 = 35 + -35

Combine like terms: -9 + -35 = -44
-44 + 5x + 6x2 = 35 + -35

Combine like terms: 35 + -35 = 0
-44 + 5x + 6x2 = 0

Begin completing the square.  Divide all terms by
6 the coefficient of the squared term: 

Divide each side by '6'.
-7.333333333 + 0.8333333333x + x2 = 0

Move the constant term to the right:

Add '7.333333333' to each side of the equation.
-7.333333333 + 0.8333333333x + 7.333333333 + x2 = 0 + 7.333333333

Reorder the terms:
-7.333333333 + 7.333333333 + 0.8333333333x + x2 = 0 + 7.333333333

Combine like terms: -7.333333333 + 7.333333333 = 0.000000000
0.000000000 + 0.8333333333x + x2 = 0 + 7.333333333
0.8333333333x + x2 = 0 + 7.333333333

Combine like terms: 0 + 7.333333333 = 7.333333333
0.8333333333x + x2 = 7.333333333

The x term is 0.8333333333x.  Take half its coefficient (0.4166666667).
Square it (0.1736111111) and add it to both sides.

Add '0.1736111111' to each side of the equation.
0.8333333333x + 0.1736111111 + x2 = 7.333333333 + 0.1736111111

Reorder the terms:
0.1736111111 + 0.8333333333x + x2 = 7.333333333 + 0.1736111111

Combine like terms: 7.333333333 + 0.1736111111 = 7.5069444441
0.1736111111 + 0.8333333333x + x2 = 7.5069444441

Factor a perfect square on the left side:
(x + 0.4166666667)(x + 0.4166666667) = 7.5069444441

Calculate the square root of the right side: 2.73988037

Break this problem into two subproblems by setting 
(x + 0.4166666667) equal to 2.73988037 and -2.73988037.


Subproblem 1
x + 0.4166666667 = 2.73988037

Simplifying
x + 0.4166666667 = 2.73988037

Reorder the terms:
0.4166666667 + x = 2.73988037

Solving
0.4166666667 + x = 2.73988037

Solving for variable 'x'.

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

Add '-0.4166666667' to each side of the equation.
0.4166666667 + -0.4166666667 + x = 2.73988037 + -0.4166666667

Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000
0.0000000000 + x = 2.73988037 + -0.4166666667
x = 2.73988037 + -0.4166666667

Combine like terms: 2.73988037 + -0.4166666667 = 2.3232137033
x = 2.3232137033

Simplifying
x = 2.3232137033


Subproblem 2
x + 0.4166666667 = -2.73988037

Simplifying
x + 0.4166666667 = -2.73988037

Reorder the terms:
0.4166666667 + x = -2.73988037

Solving
0.4166666667 + x = -2.73988037

Solving for variable 'x'.

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

Add '-0.4166666667' to each side of the equation.
0.4166666667 + -0.4166666667 + x = -2.73988037 + -0.4166666667

Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000
0.0000000000 + x = -2.73988037 + -0.4166666667
x = -2.73988037 + -0.4166666667

Combine like terms: -2.73988037 + -0.4166666667 = -3.1565470367
x = -3.1565470367

Simplifying
x = -3.1565470367


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.3232137033, -3.1565470367}

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