58x^2+86x+65=35

Solution for 58x^2+86x+65=35 equation:

Simplifying
58x2 + 86x + 65 = 35

Reorder the terms:
65 + 86x + 58x2 = 35

Solving
65 + 86x + 58x2 = 35

Solving for variable 'x'.

Reorder the terms:
65 + -35 + 86x + 58x2 = 35 + -35

Combine like terms: 65 + -35 = 30
30 + 86x + 58x2 = 35 + -35

Combine like terms: 35 + -35 = 0
30 + 86x + 58x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + 43x + 29x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(15 + 43x + 29x2)' equal to zero and attempt to solve:

Simplifying
15 + 43x + 29x2 = 0

Solving
15 + 43x + 29x2 = 0

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

Divide each side by '29'.
0.5172413793 + 1.482758621x + x2 = 0

Move the constant term to the right:

Add '-0.5172413793' to each side of the equation.
0.5172413793 + 1.482758621x + -0.5172413793 + x2 = 0 + -0.5172413793

Reorder the terms:
0.5172413793 + -0.5172413793 + 1.482758621x + x2 = 0 + -0.5172413793

Combine like terms: 0.5172413793 + -0.5172413793 = 0.0000000000
0.0000000000 + 1.482758621x + x2 = 0 + -0.5172413793
1.482758621x + x2 = 0 + -0.5172413793

Combine like terms: 0 + -0.5172413793 = -0.5172413793
1.482758621x + x2 = -0.5172413793

The x term is 1.482758621x.  Take half its coefficient (0.7413793105).
Square it (0.5496432820) and add it to both sides.

Add '0.5496432820' to each side of the equation.
1.482758621x + 0.5496432820 + x2 = -0.5172413793 + 0.5496432820

Reorder the terms:
0.5496432820 + 1.482758621x + x2 = -0.5172413793 + 0.5496432820

Combine like terms: -0.5172413793 + 0.5496432820 = 0.0324019027
0.5496432820 + 1.482758621x + x2 = 0.0324019027

Factor a perfect square on the left side:
(x + 0.7413793105)(x + 0.7413793105) = 0.0324019027

Calculate the square root of the right side: 0.180005285

Break this problem into two subproblems by setting 
(x + 0.7413793105) equal to 0.180005285 and -0.180005285.

Subproblem 1
x + 0.7413793105 = 0.180005285

Simplifying
x + 0.7413793105 = 0.180005285

Reorder the terms:
0.7413793105 + x = 0.180005285

Solving
0.7413793105 + x = 0.180005285

Solving for variable 'x'.

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

Add '-0.7413793105' to each side of the equation.
0.7413793105 + -0.7413793105 + x = 0.180005285 + -0.7413793105

Combine like terms: 0.7413793105 + -0.7413793105 = 0.0000000000
0.0000000000 + x = 0.180005285 + -0.7413793105
x = 0.180005285 + -0.7413793105

Combine like terms: 0.180005285 + -0.7413793105 = -0.5613740255
x = -0.5613740255

Simplifying
x = -0.5613740255

Subproblem 2
x + 0.7413793105 = -0.180005285

Simplifying
x + 0.7413793105 = -0.180005285

Reorder the terms:
0.7413793105 + x = -0.180005285

Solving
0.7413793105 + x = -0.180005285

Solving for variable 'x'.

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

Add '-0.7413793105' to each side of the equation.
0.7413793105 + -0.7413793105 + x = -0.180005285 + -0.7413793105

Combine like terms: 0.7413793105 + -0.7413793105 = 0.0000000000
0.0000000000 + x = -0.180005285 + -0.7413793105
x = -0.180005285 + -0.7413793105

Combine like terms: -0.180005285 + -0.7413793105 = -0.9213845955
x = -0.9213845955

Simplifying
x = -0.9213845955

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.5613740255, -0.9213845955}
Solution
x = {-0.5613740255, -0.9213845955}