F(0)=x^2+12x-35

Solution for F(0)=x^2+12x-35 equation:

Simplifying
F(0) = x2 + 12x + -35

Reorder the terms for easier multiplication:
0F = x2 + 12x + -35

Anything times zero is zero.
0F = x2 + 12x + -35

Reorder the terms:
0 = -35 + 12x + x2

Solving
0 = -35 + 12x + x2

Solving for variable 'x'.

Combine like terms: 0 + 35 = 35
35 + -12x + -1x2 = -35 + 12x + x2 + 35 + -12x + -1x2

Reorder the terms:
35 + -12x + -1x2 = -35 + 35 + 12x + -12x + x2 + -1x2

Combine like terms: -35 + 35 = 0
35 + -12x + -1x2 = 0 + 12x + -12x + x2 + -1x2
35 + -12x + -1x2 = 12x + -12x + x2 + -1x2

Combine like terms: 12x + -12x = 0
35 + -12x + -1x2 = 0 + x2 + -1x2
35 + -12x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
35 + -12x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-35 + 12x + x2 = 0

Move the constant term to the right:

Add '35' to each side of the equation.
-35 + 12x + 35 + x2 = 0 + 35

Reorder the terms:
-35 + 35 + 12x + x2 = 0 + 35

Combine like terms: -35 + 35 = 0
0 + 12x + x2 = 0 + 35
12x + x2 = 0 + 35

Combine like terms: 0 + 35 = 35
12x + x2 = 35

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 35 + 36

Reorder the terms:
36 + 12x + x2 = 35 + 36

Combine like terms: 35 + 36 = 71
36 + 12x + x2 = 71

Factor a perfect square on the left side:
(x + 6)(x + 6) = 71

Calculate the square root of the right side: 8.426149773

Break this problem into two subproblems by setting 
(x + 6) equal to 8.426149773 and -8.426149773.

Subproblem 1
x + 6 = 8.426149773

Simplifying
x + 6 = 8.426149773

Reorder the terms:
6 + x = 8.426149773

Solving
6 + x = 8.426149773

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + x = 8.426149773 + -6

Combine like terms: 6 + -6 = 0
0 + x = 8.426149773 + -6
x = 8.426149773 + -6

Combine like terms: 8.426149773 + -6 = 2.426149773
x = 2.426149773

Simplifying
x = 2.426149773

Subproblem 2
x + 6 = -8.426149773

Simplifying
x + 6 = -8.426149773

Reorder the terms:
6 + x = -8.426149773

Solving
6 + x = -8.426149773

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + x = -8.426149773 + -6

Combine like terms: 6 + -6 = 0
0 + x = -8.426149773 + -6
x = -8.426149773 + -6

Combine like terms: -8.426149773 + -6 = -14.426149773
x = -14.426149773

Simplifying
x = -14.426149773

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.426149773, -14.426149773}