2x^2+24x-148=0

Solution for 2x^2+24x-148=0 equation:

Simplifying
2x2 + 24x + -148 = 0

Reorder the terms:
-148 + 24x + 2x2 = 0

Solving
-148 + 24x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-74 + 12x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-74 + 12x + x2)' equal to zero and attempt to solve:

Simplifying
-74 + 12x + x2 = 0

Solving
-74 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '74' to each side of the equation.
-74 + 12x + 74 + x2 = 0 + 74

Reorder the terms:
-74 + 74 + 12x + x2 = 0 + 74

Combine like terms: -74 + 74 = 0
0 + 12x + x2 = 0 + 74
12x + x2 = 0 + 74

Combine like terms: 0 + 74 = 74
12x + x2 = 74

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 74 + 36

Reorder the terms:
36 + 12x + x2 = 74 + 36

Combine like terms: 74 + 36 = 110
36 + 12x + x2 = 110

Factor a perfect square on the left side:
(x + 6)(x + 6) = 110

Calculate the square root of the right side: 10.488088482

Break this problem into two subproblems by setting 
(x + 6) equal to 10.488088482 and -10.488088482.

Subproblem 1
x + 6 = 10.488088482

Simplifying
x + 6 = 10.488088482

Reorder the terms:
6 + x = 10.488088482

Solving
6 + x = 10.488088482

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = 10.488088482 + -6

Combine like terms: 6 + -6 = 0
0 + x = 10.488088482 + -6
x = 10.488088482 + -6

Combine like terms: 10.488088482 + -6 = 4.488088482
x = 4.488088482

Simplifying
x = 4.488088482

Subproblem 2
x + 6 = -10.488088482

Simplifying
x + 6 = -10.488088482

Reorder the terms:
6 + x = -10.488088482

Solving
6 + x = -10.488088482

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = -10.488088482 + -6

Combine like terms: 6 + -6 = 0
0 + x = -10.488088482 + -6
x = -10.488088482 + -6

Combine like terms: -10.488088482 + -6 = -16.488088482
x = -16.488088482

Simplifying
x = -16.488088482

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.488088482, -16.488088482}
Solution
x = {4.488088482, -16.488088482}