-x^2-7x=7

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


Simplifying
-1x2 + -7x = 7

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

Solving
-7x + -1x2 = 7

Solving for variable 'x'.

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

Combine like terms: 7 + -7 = 0
-7 + -7x + -1x2 = 0

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

Ignore the factor -1.

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

Simplifying
7 + 7x + x2 = 0

Solving
7 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = -7 + 12.25

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

Combine like terms: -7 + 12.25 = 5.25
12.25 + 7x + x2 = 5.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(x + 3.5) equal to 2.291287847 and -2.291287847.


Subproblem 1
x + 3.5 = 2.291287847

Simplifying
x + 3.5 = 2.291287847

Reorder the terms:
3.5 + x = 2.291287847

Solving
3.5 + x = 2.291287847

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 = 2.291287847 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 2.291287847 + -3.5
x = 2.291287847 + -3.5

Combine like terms: 2.291287847 + -3.5 = -1.208712153
x = -1.208712153

Simplifying
x = -1.208712153


Subproblem 2
x + 3.5 = -2.291287847

Simplifying
x + 3.5 = -2.291287847

Reorder the terms:
3.5 + x = -2.291287847

Solving
3.5 + x = -2.291287847

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 = -2.291287847 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -2.291287847 + -3.5
x = -2.291287847 + -3.5

Combine like terms: -2.291287847 + -3.5 = -5.791287847
x = -5.791287847

Simplifying
x = -5.791287847


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.208712153, -5.791287847}
Solution
x = {-1.208712153, -5.791287847}

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