-2=x^2+7x+1

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Solution for -2=x^2+7x+1 equation: 


Simplifying
-2 = x2 + 7x + 1

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

Solving
-2 = 1 + 7x + x2

Solving for variable 'x'.

Combine like terms: -2 + -1 = -3
-3 + -7x + -1x2 = 1 + 7x + x2 + -1 + -7x + -1x2

Reorder the terms:
-3 + -7x + -1x2 = 1 + -1 + 7x + -7x + x2 + -1x2

Combine like terms: 1 + -1 = 0
-3 + -7x + -1x2 = 0 + 7x + -7x + x2 + -1x2
-3 + -7x + -1x2 = 7x + -7x + x2 + -1x2

Combine like terms: 7x + -7x = 0
-3 + -7x + -1x2 = 0 + x2 + -1x2
-3 + -7x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-3 + -7x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 7x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(3 + 7x + x2)' equal to zero and attempt to solve:

Simplifying
3 + 7x + x2 = 0

Solving
3 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 7x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + 7x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 7x + x2 = 0 + -3
7x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
7x + x2 = -3

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 = -3 + 12.25

Reorder the terms:
12.25 + 7x + x2 = -3 + 12.25

Combine like terms: -3 + 12.25 = 9.25
12.25 + 7x + x2 = 9.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(x + 3.5) equal to 3.041381265 and -3.041381265.


Subproblem 1
x + 3.5 = 3.041381265

Simplifying
x + 3.5 = 3.041381265

Reorder the terms:
3.5 + x = 3.041381265

Solving
3.5 + x = 3.041381265

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 = 3.041381265 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 3.041381265 + -3.5
x = 3.041381265 + -3.5

Combine like terms: 3.041381265 + -3.5 = -0.458618735
x = -0.458618735

Simplifying
x = -0.458618735


Subproblem 2
x + 3.5 = -3.041381265

Simplifying
x + 3.5 = -3.041381265

Reorder the terms:
3.5 + x = -3.041381265

Solving
3.5 + x = -3.041381265

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 = -3.041381265 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -3.041381265 + -3.5
x = -3.041381265 + -3.5

Combine like terms: -3.041381265 + -3.5 = -6.541381265
x = -6.541381265

Simplifying
x = -6.541381265


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.458618735, -6.541381265}
Solution
x = {-0.458618735, -6.541381265}

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