x^2+14x-35=0

Solution for x^2+14x-35=0 equation:

Simplifying
x2 + 14x + -35 = 0

Reorder the terms:
-35 + 14x + x2 = 0

Solving
-35 + 14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '35' to each side of the equation.
-35 + 14x + 35 + x2 = 0 + 35

Reorder the terms:
-35 + 35 + 14x + x2 = 0 + 35

Combine like terms: -35 + 35 = 0
0 + 14x + x2 = 0 + 35
14x + x2 = 0 + 35

Combine like terms: 0 + 35 = 35
14x + x2 = 35

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = 35 + 49

Reorder the terms:
49 + 14x + x2 = 35 + 49

Combine like terms: 35 + 49 = 84
49 + 14x + x2 = 84

Factor a perfect square on the left side:
(x + 7)(x + 7) = 84

Calculate the square root of the right side: 9.16515139

Break this problem into two subproblems by setting 
(x + 7) equal to 9.16515139 and -9.16515139.

Subproblem 1
x + 7 = 9.16515139

Simplifying
x + 7 = 9.16515139

Reorder the terms:
7 + x = 9.16515139

Solving
7 + x = 9.16515139

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = 9.16515139 + -7

Combine like terms: 7 + -7 = 0
0 + x = 9.16515139 + -7
x = 9.16515139 + -7

Combine like terms: 9.16515139 + -7 = 2.16515139
x = 2.16515139

Simplifying
x = 2.16515139

Subproblem 2
x + 7 = -9.16515139

Simplifying
x + 7 = -9.16515139

Reorder the terms:
7 + x = -9.16515139

Solving
7 + x = -9.16515139

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = -9.16515139 + -7

Combine like terms: 7 + -7 = 0
0 + x = -9.16515139 + -7
x = -9.16515139 + -7

Combine like terms: -9.16515139 + -7 = -16.16515139
x = -16.16515139

Simplifying
x = -16.16515139

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.16515139, -16.16515139}