-x^2-14x-43=0

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Solution for -x^2-14x-43=0 equation: 


Simplifying
-1x2 + -14x + -43 = 0

Reorder the terms:
-43 + -14x + -1x2 = 0

Solving
-43 + -14x + -1x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(43 + 14x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(43 + 14x + x2)' equal to zero and attempt to solve:

Simplifying
43 + 14x + x2 = 0

Solving
43 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-43' to each side of the equation.
43 + 14x + -43 + x2 = 0 + -43

Reorder the terms:
43 + -43 + 14x + x2 = 0 + -43

Combine like terms: 43 + -43 = 0
0 + 14x + x2 = 0 + -43
14x + x2 = 0 + -43

Combine like terms: 0 + -43 = -43
14x + x2 = -43

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 = -43 + 49

Reorder the terms:
49 + 14x + x2 = -43 + 49

Combine like terms: -43 + 49 = 6
49 + 14x + x2 = 6

Factor a perfect square on the left side:
(x + 7)(x + 7) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(x + 7) equal to 2.449489743 and -2.449489743.


Subproblem 1
x + 7 = 2.449489743

Simplifying
x + 7 = 2.449489743

Reorder the terms:
7 + x = 2.449489743

Solving
7 + x = 2.449489743

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 = 2.449489743 + -7

Combine like terms: 7 + -7 = 0
0 + x = 2.449489743 + -7
x = 2.449489743 + -7

Combine like terms: 2.449489743 + -7 = -4.550510257
x = -4.550510257

Simplifying
x = -4.550510257


Subproblem 2
x + 7 = -2.449489743

Simplifying
x + 7 = -2.449489743

Reorder the terms:
7 + x = -2.449489743

Solving
7 + x = -2.449489743

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 = -2.449489743 + -7

Combine like terms: 7 + -7 = 0
0 + x = -2.449489743 + -7
x = -2.449489743 + -7

Combine like terms: -2.449489743 + -7 = -9.449489743
x = -9.449489743

Simplifying
x = -9.449489743


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-4.550510257, -9.449489743}
Solution
x = {-4.550510257, -9.449489743}

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