(x-14)(x-3)=10

Solution for (x-14)(x-3)=10 equation:

Simplifying
(x + -14)(x + -3) = 10

Reorder the terms:
(-14 + x)(x + -3) = 10

Reorder the terms:
(-14 + x)(-3 + x) = 10

Multiply (-14 + x) * (-3 + x)
(-14(-3 + x) + x(-3 + x)) = 10
((-3 * -14 + x * -14) + x(-3 + x)) = 10
((42 + -14x) + x(-3 + x)) = 10
(42 + -14x + (-3 * x + x * x)) = 10
(42 + -14x + (-3x + x2)) = 10

Combine like terms: -14x + -3x = -17x
(42 + -17x + x2) = 10

Solving
42 + -17x + x2 = 10

Solving for variable 'x'.

Reorder the terms:
42 + -10 + -17x + x2 = 10 + -10

Combine like terms: 42 + -10 = 32
32 + -17x + x2 = 10 + -10

Combine like terms: 10 + -10 = 0
32 + -17x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-32' to each side of the equation.
32 + -17x + -32 + x2 = 0 + -32

Reorder the terms:
32 + -32 + -17x + x2 = 0 + -32

Combine like terms: 32 + -32 = 0
0 + -17x + x2 = 0 + -32
-17x + x2 = 0 + -32

Combine like terms: 0 + -32 = -32
-17x + x2 = -32

The x term is -17x.  Take half its coefficient (-8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
-17x + 72.25 + x2 = -32 + 72.25

Reorder the terms:
72.25 + -17x + x2 = -32 + 72.25

Combine like terms: -32 + 72.25 = 40.25
72.25 + -17x + x2 = 40.25

Factor a perfect square on the left side:
(x + -8.5)(x + -8.5) = 40.25

Calculate the square root of the right side: 6.34428877

Break this problem into two subproblems by setting 
(x + -8.5) equal to 6.34428877 and -6.34428877.

Subproblem 1
x + -8.5 = 6.34428877

Simplifying
x + -8.5 = 6.34428877

Reorder the terms:
-8.5 + x = 6.34428877

Solving
-8.5 + x = 6.34428877

Solving for variable 'x'.

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

Add '8.5' to each side of the equation.
-8.5 + 8.5 + x = 6.34428877 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + x = 6.34428877 + 8.5
x = 6.34428877 + 8.5

Combine like terms: 6.34428877 + 8.5 = 14.84428877
x = 14.84428877

Simplifying
x = 14.84428877

Subproblem 2
x + -8.5 = -6.34428877

Simplifying
x + -8.5 = -6.34428877

Reorder the terms:
-8.5 + x = -6.34428877

Solving
-8.5 + x = -6.34428877

Solving for variable 'x'.

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

Add '8.5' to each side of the equation.
-8.5 + 8.5 + x = -6.34428877 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + x = -6.34428877 + 8.5
x = -6.34428877 + 8.5

Combine like terms: -6.34428877 + 8.5 = 2.15571123
x = 2.15571123

Simplifying
x = 2.15571123

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.84428877, 2.15571123}