-2x^2-28x-9=0

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Solution for -2x^2-28x-9=0 equation: 


Simplifying
-2x2 + -28x + -9 = 0

Reorder the terms:
-9 + -28x + -2x2 = 0

Solving
-9 + -28x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(9 + 28x + 2x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(9 + 28x + 2x2)' equal to zero and attempt to solve:

Simplifying
9 + 28x + 2x2 = 0

Solving
9 + 28x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
4.5 + 14x + x2 = 0

Move the constant term to the right:

Add '-4.5' to each side of the equation.
4.5 + 14x + -4.5 + x2 = 0 + -4.5

Reorder the terms:
4.5 + -4.5 + 14x + x2 = 0 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + 14x + x2 = 0 + -4.5
14x + x2 = 0 + -4.5

Combine like terms: 0 + -4.5 = -4.5
14x + x2 = -4.5

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 = -4.5 + 49

Reorder the terms:
49 + 14x + x2 = -4.5 + 49

Combine like terms: -4.5 + 49 = 44.5
49 + 14x + x2 = 44.5

Factor a perfect square on the left side:
(x + 7)(x + 7) = 44.5

Calculate the square root of the right side: 6.670832032

Break this problem into two subproblems by setting 
(x + 7) equal to 6.670832032 and -6.670832032.


Subproblem 1
x + 7 = 6.670832032

Simplifying
x + 7 = 6.670832032

Reorder the terms:
7 + x = 6.670832032

Solving
7 + x = 6.670832032

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 = 6.670832032 + -7

Combine like terms: 7 + -7 = 0
0 + x = 6.670832032 + -7
x = 6.670832032 + -7

Combine like terms: 6.670832032 + -7 = -0.329167968
x = -0.329167968

Simplifying
x = -0.329167968


Subproblem 2
x + 7 = -6.670832032

Simplifying
x + 7 = -6.670832032

Reorder the terms:
7 + x = -6.670832032

Solving
7 + x = -6.670832032

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 = -6.670832032 + -7

Combine like terms: 7 + -7 = 0
0 + x = -6.670832032 + -7
x = -6.670832032 + -7

Combine like terms: -6.670832032 + -7 = -13.670832032
x = -13.670832032

Simplifying
x = -13.670832032


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.329167968, -13.670832032}
Solution
x = {-0.329167968, -13.670832032}

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