35=(x-14)(x-5)

Solution for 35=(x-14)(x-5) equation:

Simplifying
35 = (x + -14)(x + -5)

Reorder the terms:
35 = (-14 + x)(x + -5)

Reorder the terms:
35 = (-14 + x)(-5 + x)

Multiply (-14 + x) * (-5 + x)
35 = (-14(-5 + x) + x(-5 + x))
35 = ((-5 * -14 + x * -14) + x(-5 + x))
35 = ((70 + -14x) + x(-5 + x))
35 = (70 + -14x + (-5 * x + x * x))
35 = (70 + -14x + (-5x + x2))

Combine like terms: -14x + -5x = -19x
35 = (70 + -19x + x2)

Solving
35 = 70 + -19x + x2

Solving for variable 'x'.

Combine like terms: 35 + -70 = -35
-35 + 19x + -1x2 = 70 + -19x + x2 + -70 + 19x + -1x2

Reorder the terms:
-35 + 19x + -1x2 = 70 + -70 + -19x + 19x + x2 + -1x2

Combine like terms: 70 + -70 = 0
-35 + 19x + -1x2 = 0 + -19x + 19x + x2 + -1x2
-35 + 19x + -1x2 = -19x + 19x + x2 + -1x2

Combine like terms: -19x + 19x = 0
-35 + 19x + -1x2 = 0 + x2 + -1x2
-35 + 19x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-35 + 19x + -1x2 = 0

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

Divide each side by '-1'.
35 + -19x + x2 = 0

Move the constant term to the right:

Add '-35' to each side of the equation.
35 + -19x + -35 + x2 = 0 + -35

Reorder the terms:
35 + -35 + -19x + x2 = 0 + -35

Combine like terms: 35 + -35 = 0
0 + -19x + x2 = 0 + -35
-19x + x2 = 0 + -35

Combine like terms: 0 + -35 = -35
-19x + x2 = -35

The x term is -19x.  Take half its coefficient (-9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
-19x + 90.25 + x2 = -35 + 90.25

Reorder the terms:
90.25 + -19x + x2 = -35 + 90.25

Combine like terms: -35 + 90.25 = 55.25
90.25 + -19x + x2 = 55.25

Factor a perfect square on the left side:
(x + -9.5)(x + -9.5) = 55.25

Calculate the square root of the right side: 7.433034374

Break this problem into two subproblems by setting 
(x + -9.5) equal to 7.433034374 and -7.433034374.

Subproblem 1
x + -9.5 = 7.433034374

Simplifying
x + -9.5 = 7.433034374

Reorder the terms:
-9.5 + x = 7.433034374

Solving
-9.5 + x = 7.433034374

Solving for variable 'x'.

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

Add '9.5' to each side of the equation.
-9.5 + 9.5 + x = 7.433034374 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + x = 7.433034374 + 9.5
x = 7.433034374 + 9.5

Combine like terms: 7.433034374 + 9.5 = 16.933034374
x = 16.933034374

Simplifying
x = 16.933034374

Subproblem 2
x + -9.5 = -7.433034374

Simplifying
x + -9.5 = -7.433034374

Reorder the terms:
-9.5 + x = -7.433034374

Solving
-9.5 + x = -7.433034374

Solving for variable 'x'.

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

Add '9.5' to each side of the equation.
-9.5 + 9.5 + x = -7.433034374 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + x = -7.433034374 + 9.5
x = -7.433034374 + 9.5

Combine like terms: -7.433034374 + 9.5 = 2.066965626
x = 2.066965626

Simplifying
x = 2.066965626

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.933034374, 2.066965626}