2x^2+2x-58=0

Solution for 2x^2+2x-58=0 equation:

Simplifying
2x2 + 2x + -58 = 0

Reorder the terms:
-58 + 2x + 2x2 = 0

Solving
-58 + 2x + 2x2 = 0

Solving for variable 'x'.

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

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

Simplifying
-29 + x + x2 = 0

Solving
-29 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '29' to each side of the equation.
-29 + x + 29 + x2 = 0 + 29

Reorder the terms:
-29 + 29 + x + x2 = 0 + 29

Combine like terms: -29 + 29 = 0
0 + x + x2 = 0 + 29
x + x2 = 0 + 29

Combine like terms: 0 + 29 = 29
x + x2 = 29

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 29 + 0.25

Reorder the terms:
0.25 + x + x2 = 29 + 0.25

Combine like terms: 29 + 0.25 = 29.25
0.25 + x + x2 = 29.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 29.25

Calculate the square root of the right side: 5.408326913

Break this problem into two subproblems by setting 
(x + 0.5) equal to 5.408326913 and -5.408326913.

Subproblem 1
x + 0.5 = 5.408326913

Simplifying
x + 0.5 = 5.408326913

Reorder the terms:
0.5 + x = 5.408326913

Solving
0.5 + x = 5.408326913

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 5.408326913 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 5.408326913 + -0.5
x = 5.408326913 + -0.5

Combine like terms: 5.408326913 + -0.5 = 4.908326913
x = 4.908326913

Simplifying
x = 4.908326913

Subproblem 2
x + 0.5 = -5.408326913

Simplifying
x + 0.5 = -5.408326913

Reorder the terms:
0.5 + x = -5.408326913

Solving
0.5 + x = -5.408326913

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -5.408326913 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -5.408326913 + -0.5
x = -5.408326913 + -0.5

Combine like terms: -5.408326913 + -0.5 = -5.908326913
x = -5.908326913

Simplifying
x = -5.908326913

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.908326913, -5.908326913}
Solution
x = {4.908326913, -5.908326913}