4x^2+36x-35=115

Solution for 4x^2+36x-35=115 equation:

Simplifying
4x2 + 36x + -35 = 115

Reorder the terms:
-35 + 36x + 4x2 = 115

Solving
-35 + 36x + 4x2 = 115

Solving for variable 'x'.

Reorder the terms:
-35 + -115 + 36x + 4x2 = 115 + -115

Combine like terms: -35 + -115 = -150
-150 + 36x + 4x2 = 115 + -115

Combine like terms: 115 + -115 = 0
-150 + 36x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-75 + 18x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-75 + 18x + 2x2)' equal to zero and attempt to solve:

Simplifying
-75 + 18x + 2x2 = 0

Solving
-75 + 18x + 2x2 = 0

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

Divide each side by '2'.
-37.5 + 9x + x2 = 0

Move the constant term to the right:

Add '37.5' to each side of the equation.
-37.5 + 9x + 37.5 + x2 = 0 + 37.5

Reorder the terms:
-37.5 + 37.5 + 9x + x2 = 0 + 37.5

Combine like terms: -37.5 + 37.5 = 0.0
0.0 + 9x + x2 = 0 + 37.5
9x + x2 = 0 + 37.5

Combine like terms: 0 + 37.5 = 37.5
9x + x2 = 37.5

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = 37.5 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 37.5 + 20.25

Combine like terms: 37.5 + 20.25 = 57.75
20.25 + 9x + x2 = 57.75

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 57.75

Calculate the square root of the right side: 7.599342077

Break this problem into two subproblems by setting 
(x + 4.5) equal to 7.599342077 and -7.599342077.

Subproblem 1
x + 4.5 = 7.599342077

Simplifying
x + 4.5 = 7.599342077

Reorder the terms:
4.5 + x = 7.599342077

Solving
4.5 + x = 7.599342077

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 7.599342077 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 7.599342077 + -4.5
x = 7.599342077 + -4.5

Combine like terms: 7.599342077 + -4.5 = 3.099342077
x = 3.099342077

Simplifying
x = 3.099342077

Subproblem 2
x + 4.5 = -7.599342077

Simplifying
x + 4.5 = -7.599342077

Reorder the terms:
4.5 + x = -7.599342077

Solving
4.5 + x = -7.599342077

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -7.599342077 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -7.599342077 + -4.5
x = -7.599342077 + -4.5

Combine like terms: -7.599342077 + -4.5 = -12.099342077
x = -12.099342077

Simplifying
x = -12.099342077

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.099342077, -12.099342077}
Solution
x = {3.099342077, -12.099342077}