2x^2-12x-58=0

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Solution for 2x^2-12x-58=0 equation: 


Simplifying
2x2 + -12x + -58 = 0

Reorder the terms:
-58 + -12x + 2x2 = 0

Solving
-58 + -12x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-29 + -6x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-29 + -6x + x2)' equal to zero and attempt to solve:

Simplifying
-29 + -6x + x2 = 0

Solving
-29 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '29' to each side of the equation.
-29 + -6x + 29 + x2 = 0 + 29

Reorder the terms:
-29 + 29 + -6x + x2 = 0 + 29

Combine like terms: -29 + 29 = 0
0 + -6x + x2 = 0 + 29
-6x + x2 = 0 + 29

Combine like terms: 0 + 29 = 29
-6x + x2 = 29

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 29 + 9

Reorder the terms:
9 + -6x + x2 = 29 + 9

Combine like terms: 29 + 9 = 38
9 + -6x + x2 = 38

Factor a perfect square on the left side:
(x + -3)(x + -3) = 38

Calculate the square root of the right side: 6.164414003

Break this problem into two subproblems by setting 
(x + -3) equal to 6.164414003 and -6.164414003.


Subproblem 1
x + -3 = 6.164414003

Simplifying
x + -3 = 6.164414003

Reorder the terms:
-3 + x = 6.164414003

Solving
-3 + x = 6.164414003

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 6.164414003 + 3

Combine like terms: -3 + 3 = 0
0 + x = 6.164414003 + 3
x = 6.164414003 + 3

Combine like terms: 6.164414003 + 3 = 9.164414003
x = 9.164414003

Simplifying
x = 9.164414003


Subproblem 2
x + -3 = -6.164414003

Simplifying
x + -3 = -6.164414003

Reorder the terms:
-3 + x = -6.164414003

Solving
-3 + x = -6.164414003

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -6.164414003 + 3

Combine like terms: -3 + 3 = 0
0 + x = -6.164414003 + 3
x = -6.164414003 + 3

Combine like terms: -6.164414003 + 3 = -3.164414003
x = -3.164414003

Simplifying
x = -3.164414003


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.164414003, -3.164414003}
Solution
x = {9.164414003, -3.164414003}

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