-x^2-7x-2=0

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Solution for -x^2-7x-2=0 equation:


Simplifying
-1x2 + -7x + -2 = 0

Reorder the terms:
-2 + -7x + -1x2 = 0

Solving
-2 + -7x + -1x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2 + 7x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(2 + 7x + x2)' equal to zero and attempt to solve:

Simplifying
2 + 7x + x2 = 0

Solving
2 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 7x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + 7x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 7x + x2 = 0 + -2
7x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
7x + x2 = -2

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = -2 + 12.25

Reorder the terms:
12.25 + 7x + x2 = -2 + 12.25

Combine like terms: -2 + 12.25 = 10.25
12.25 + 7x + x2 = 10.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(x + 3.5) equal to 3.201562119 and -3.201562119.


Subproblem 1
x + 3.5 = 3.201562119

Simplifying
x + 3.5 = 3.201562119

Reorder the terms:
3.5 + x = 3.201562119

Solving
3.5 + x = 3.201562119

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 3.201562119 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 3.201562119 + -3.5
x = 3.201562119 + -3.5

Combine like terms: 3.201562119 + -3.5 = -0.298437881
x = -0.298437881

Simplifying
x = -0.298437881


Subproblem 2
x + 3.5 = -3.201562119

Simplifying
x + 3.5 = -3.201562119

Reorder the terms:
3.5 + x = -3.201562119

Solving
3.5 + x = -3.201562119

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -3.201562119 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -3.201562119 + -3.5
x = -3.201562119 + -3.5

Combine like terms: -3.201562119 + -3.5 = -6.701562119
x = -6.701562119

Simplifying
x = -6.701562119


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.298437881, -6.701562119}
Solution
x = {-0.298437881, -6.701562119}

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