2x^2+28x+24=0

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Solution for 2x^2+28x+24=0 equation: 


Simplifying
2x2 + 28x + 24 = 0

Reorder the terms:
24 + 28x + 2x2 = 0

Solving
24 + 28x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + 14x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(12 + 14x + x2)' equal to zero and attempt to solve:

Simplifying
12 + 14x + x2 = 0

Solving
12 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + 14x + -12 + x2 = 0 + -12

Reorder the terms:
12 + -12 + 14x + x2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + 14x + x2 = 0 + -12
14x + x2 = 0 + -12

Combine like terms: 0 + -12 = -12
14x + x2 = -12

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = -12 + 49

Reorder the terms:
49 + 14x + x2 = -12 + 49

Combine like terms: -12 + 49 = 37
49 + 14x + x2 = 37

Factor a perfect square on the left side:
(x + 7)(x + 7) = 37

Calculate the square root of the right side: 6.08276253

Break this problem into two subproblems by setting 
(x + 7) equal to 6.08276253 and -6.08276253.


Subproblem 1
x + 7 = 6.08276253

Simplifying
x + 7 = 6.08276253

Reorder the terms:
7 + x = 6.08276253

Solving
7 + x = 6.08276253

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = 6.08276253 + -7

Combine like terms: 7 + -7 = 0
0 + x = 6.08276253 + -7
x = 6.08276253 + -7

Combine like terms: 6.08276253 + -7 = -0.91723747
x = -0.91723747

Simplifying
x = -0.91723747


Subproblem 2
x + 7 = -6.08276253

Simplifying
x + 7 = -6.08276253

Reorder the terms:
7 + x = -6.08276253

Solving
7 + x = -6.08276253

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = -6.08276253 + -7

Combine like terms: 7 + -7 = 0
0 + x = -6.08276253 + -7
x = -6.08276253 + -7

Combine like terms: -6.08276253 + -7 = -13.08276253
x = -13.08276253

Simplifying
x = -13.08276253


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.91723747, -13.08276253}
Solution
x = {-0.91723747, -13.08276253}

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