x^2+7x=-3.5

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Solution for x^2+7x=-3.5 equation: 


Simplifying
x2 + 7x = -3.5

Reorder the terms:
7x + x2 = -3.5

Solving
7x + x2 = -3.5

Solving for variable 'x'.

Reorder the terms:
3.5 + 7x + x2 = -3.5 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
3.5 + 7x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + 7x + -3.5 + x2 = 0.0 + -3.5

Reorder the terms:
3.5 + -3.5 + 7x + x2 = 0.0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + 7x + x2 = 0.0 + -3.5
7x + x2 = 0.0 + -3.5

Combine like terms: 0.0 + -3.5 = -3.5
7x + x2 = -3.5

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 = -3.5 + 12.25

Reorder the terms:
12.25 + 7x + x2 = -3.5 + 12.25

Combine like terms: -3.5 + 12.25 = 8.75
12.25 + 7x + x2 = 8.75

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 8.75

Calculate the square root of the right side: 2.958039892

Break this problem into two subproblems by setting 
(x + 3.5) equal to 2.958039892 and -2.958039892.


Subproblem 1
x + 3.5 = 2.958039892

Simplifying
x + 3.5 = 2.958039892

Reorder the terms:
3.5 + x = 2.958039892

Solving
3.5 + x = 2.958039892

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 = 2.958039892 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 2.958039892 + -3.5
x = 2.958039892 + -3.5

Combine like terms: 2.958039892 + -3.5 = -0.541960108
x = -0.541960108

Simplifying
x = -0.541960108


Subproblem 2
x + 3.5 = -2.958039892

Simplifying
x + 3.5 = -2.958039892

Reorder the terms:
3.5 + x = -2.958039892

Solving
3.5 + x = -2.958039892

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 = -2.958039892 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -2.958039892 + -3.5
x = -2.958039892 + -3.5

Combine like terms: -2.958039892 + -3.5 = -6.458039892
x = -6.458039892

Simplifying
x = -6.458039892


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.541960108, -6.458039892}

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