2x^2+20x+24=0

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Solution for 2x^2+20x+24=0 equation: 


Simplifying
2x2 + 20x + 24 = 0

Reorder the terms:
24 + 20x + 2x2 = 0

Solving
24 + 20x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + 10x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(12 + 10x + x2)' equal to zero and attempt to solve:

Simplifying
12 + 10x + x2 = 0

Solving
12 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + 10x + -12 + x2 = 0 + -12

Reorder the terms:
12 + -12 + 10x + x2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + 10x + x2 = 0 + -12
10x + x2 = 0 + -12

Combine like terms: 0 + -12 = -12
10x + x2 = -12

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = -12 + 25

Reorder the terms:
25 + 10x + x2 = -12 + 25

Combine like terms: -12 + 25 = 13
25 + 10x + x2 = 13

Factor a perfect square on the left side:
(x + 5)(x + 5) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(x + 5) equal to 3.605551275 and -3.605551275.


Subproblem 1
x + 5 = 3.605551275

Simplifying
x + 5 = 3.605551275

Reorder the terms:
5 + x = 3.605551275

Solving
5 + x = 3.605551275

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 3.605551275 + -5

Combine like terms: 5 + -5 = 0
0 + x = 3.605551275 + -5
x = 3.605551275 + -5

Combine like terms: 3.605551275 + -5 = -1.394448725
x = -1.394448725

Simplifying
x = -1.394448725


Subproblem 2
x + 5 = -3.605551275

Simplifying
x + 5 = -3.605551275

Reorder the terms:
5 + x = -3.605551275

Solving
5 + x = -3.605551275

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -3.605551275 + -5

Combine like terms: 5 + -5 = 0
0 + x = -3.605551275 + -5
x = -3.605551275 + -5

Combine like terms: -3.605551275 + -5 = -8.605551275
x = -8.605551275

Simplifying
x = -8.605551275


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.394448725, -8.605551275}
Solution
x = {-1.394448725, -8.605551275}

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