(x-1)(x+13)=-35

Solution for (x-1)(x+13)=-35 equation:

Simplifying
(x + -1)(x + 13) = -35

Reorder the terms:
(-1 + x)(x + 13) = -35

Reorder the terms:
(-1 + x)(13 + x) = -35

Multiply (-1 + x) * (13 + x)
(-1(13 + x) + x(13 + x)) = -35
((13 * -1 + x * -1) + x(13 + x)) = -35
((-13 + -1x) + x(13 + x)) = -35
(-13 + -1x + (13 * x + x * x)) = -35
(-13 + -1x + (13x + x2)) = -35

Combine like terms: -1x + 13x = 12x
(-13 + 12x + x2) = -35

Solving
-13 + 12x + x2 = -35

Solving for variable 'x'.

Reorder the terms:
-13 + 35 + 12x + x2 = -35 + 35

Combine like terms: -13 + 35 = 22
22 + 12x + x2 = -35 + 35

Combine like terms: -35 + 35 = 0
22 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-22' to each side of the equation.
22 + 12x + -22 + x2 = 0 + -22

Reorder the terms:
22 + -22 + 12x + x2 = 0 + -22

Combine like terms: 22 + -22 = 0
0 + 12x + x2 = 0 + -22
12x + x2 = 0 + -22

Combine like terms: 0 + -22 = -22
12x + x2 = -22

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 = -22 + 36

Reorder the terms:
36 + 12x + x2 = -22 + 36

Combine like terms: -22 + 36 = 14
36 + 12x + x2 = 14

Factor a perfect square on the left side:
(x + 6)(x + 6) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(x + 6) equal to 3.741657387 and -3.741657387.

Subproblem 1
x + 6 = 3.741657387

Simplifying
x + 6 = 3.741657387

Reorder the terms:
6 + x = 3.741657387

Solving
6 + x = 3.741657387

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 = 3.741657387 + -6

Combine like terms: 6 + -6 = 0
0 + x = 3.741657387 + -6
x = 3.741657387 + -6

Combine like terms: 3.741657387 + -6 = -2.258342613
x = -2.258342613

Simplifying
x = -2.258342613

Subproblem 2
x + 6 = -3.741657387

Simplifying
x + 6 = -3.741657387

Reorder the terms:
6 + x = -3.741657387

Solving
6 + x = -3.741657387

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 = -3.741657387 + -6

Combine like terms: 6 + -6 = 0
0 + x = -3.741657387 + -6
x = -3.741657387 + -6

Combine like terms: -3.741657387 + -6 = -9.741657387
x = -9.741657387

Simplifying
x = -9.741657387

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.258342613, -9.741657387}