-(x^2+13x+28)=0

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Solution for -(x^2+13x+28)=0 equation: 


Simplifying
-1(x2 + 13x + 28) = 0

Reorder the terms:
-1(28 + 13x + x2) = 0
(28 * -1 + 13x * -1 + x2 * -1) = 0
(-28 + -13x + -1x2) = 0

Solving
-28 + -13x + -1x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(28 + 13x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(28 + 13x + x2)' equal to zero and attempt to solve:

Simplifying
28 + 13x + x2 = 0

Solving
28 + 13x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-28' to each side of the equation.
28 + 13x + -28 + x2 = 0 + -28

Reorder the terms:
28 + -28 + 13x + x2 = 0 + -28

Combine like terms: 28 + -28 = 0
0 + 13x + x2 = 0 + -28
13x + x2 = 0 + -28

Combine like terms: 0 + -28 = -28
13x + x2 = -28

The x term is 13x.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13x + 42.25 + x2 = -28 + 42.25

Reorder the terms:
42.25 + 13x + x2 = -28 + 42.25

Combine like terms: -28 + 42.25 = 14.25
42.25 + 13x + x2 = 14.25

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(x + 6.5) equal to 3.774917218 and -3.774917218.


Subproblem 1
x + 6.5 = 3.774917218

Simplifying
x + 6.5 = 3.774917218

Reorder the terms:
6.5 + x = 3.774917218

Solving
6.5 + x = 3.774917218

Solving for variable 'x'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + x = 3.774917218 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = 3.774917218 + -6.5
x = 3.774917218 + -6.5

Combine like terms: 3.774917218 + -6.5 = -2.725082782
x = -2.725082782

Simplifying
x = -2.725082782


Subproblem 2
x + 6.5 = -3.774917218

Simplifying
x + 6.5 = -3.774917218

Reorder the terms:
6.5 + x = -3.774917218

Solving
6.5 + x = -3.774917218

Solving for variable 'x'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + x = -3.774917218 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = -3.774917218 + -6.5
x = -3.774917218 + -6.5

Combine like terms: -3.774917218 + -6.5 = -10.274917218
x = -10.274917218

Simplifying
x = -10.274917218


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.725082782, -10.274917218}
Solution
x = {-2.725082782, -10.274917218}

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