-2(x^2+7x+10)=3.5

Solution for -2(x^2+7x+10)=3.5 equation:

Simplifying
-2(x2 + 7x + 10) = 3.5

Reorder the terms:
-2(10 + 7x + x2) = 3.5
(10 * -2 + 7x * -2 + x2 * -2) = 3.5
(-20 + -14x + -2x2) = 3.5

Solving
-20 + -14x + -2x2 = 3.5

Solving for variable 'x'.

Reorder the terms:
-20 + -3.5 + -14x + -2x2 = 3.5 + -3.5

Combine like terms: -20 + -3.5 = -23.5
-23.5 + -14x + -2x2 = 3.5 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
-23.5 + -14x + -2x2 = 0.0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
11.75 + 7x + x2 = 0.0

Move the constant term to the right:

Add '-11.75' to each side of the equation.
11.75 + 7x + -11.75 + x2 = 0.0 + -11.75

Reorder the terms:
11.75 + -11.75 + 7x + x2 = 0.0 + -11.75

Combine like terms: 11.75 + -11.75 = 0.00
0.00 + 7x + x2 = 0.0 + -11.75
7x + x2 = 0.0 + -11.75

Combine like terms: 0.0 + -11.75 = -11.75
7x + x2 = -11.75

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 = -11.75 + 12.25

Reorder the terms:
12.25 + 7x + x2 = -11.75 + 12.25

Combine like terms: -11.75 + 12.25 = 0.5
12.25 + 7x + x2 = 0.5

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 0.5

Calculate the square root of the right side: 0.707106781

Break this problem into two subproblems by setting 
(x + 3.5) equal to 0.707106781 and -0.707106781.

Subproblem 1
x + 3.5 = 0.707106781

Simplifying
x + 3.5 = 0.707106781

Reorder the terms:
3.5 + x = 0.707106781

Solving
3.5 + x = 0.707106781

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 = 0.707106781 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 0.707106781 + -3.5
x = 0.707106781 + -3.5

Combine like terms: 0.707106781 + -3.5 = -2.792893219
x = -2.792893219

Simplifying
x = -2.792893219

Subproblem 2
x + 3.5 = -0.707106781

Simplifying
x + 3.5 = -0.707106781

Reorder the terms:
3.5 + x = -0.707106781

Solving
3.5 + x = -0.707106781

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 = -0.707106781 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -0.707106781 + -3.5
x = -0.707106781 + -3.5

Combine like terms: -0.707106781 + -3.5 = -4.207106781
x = -4.207106781

Simplifying
x = -4.207106781

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.792893219, -4.207106781}