x^2+7x+6.5=0

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Solution for x^2+7x+6.5=0 equation: 


Simplifying
x2 + 7x + 6.5 = 0

Reorder the terms:
6.5 + 7x + x2 = 0

Solving
6.5 + 7x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-6.5' to each side of the equation.
6.5 + 7x + -6.5 + x2 = 0 + -6.5

Reorder the terms:
6.5 + -6.5 + 7x + x2 = 0 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + 7x + x2 = 0 + -6.5
7x + x2 = 0 + -6.5

Combine like terms: 0 + -6.5 = -6.5
7x + x2 = -6.5

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 = -6.5 + 12.25

Reorder the terms:
12.25 + 7x + x2 = -6.5 + 12.25

Combine like terms: -6.5 + 12.25 = 5.75
12.25 + 7x + x2 = 5.75

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 5.75

Calculate the square root of the right side: 2.397915762

Break this problem into two subproblems by setting 
(x + 3.5) equal to 2.397915762 and -2.397915762.


Subproblem 1
x + 3.5 = 2.397915762

Simplifying
x + 3.5 = 2.397915762

Reorder the terms:
3.5 + x = 2.397915762

Solving
3.5 + x = 2.397915762

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 = 2.397915762 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 2.397915762 + -3.5
x = 2.397915762 + -3.5

Combine like terms: 2.397915762 + -3.5 = -1.102084238
x = -1.102084238

Simplifying
x = -1.102084238


Subproblem 2
x + 3.5 = -2.397915762

Simplifying
x + 3.5 = -2.397915762

Reorder the terms:
3.5 + x = -2.397915762

Solving
3.5 + x = -2.397915762

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 = -2.397915762 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -2.397915762 + -3.5
x = -2.397915762 + -3.5

Combine like terms: -2.397915762 + -3.5 = -5.897915762
x = -5.897915762

Simplifying
x = -5.897915762


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.102084238, -5.897915762}

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