(x+1)(x+18)=10

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Solution for (x+1)(x+18)=10 equation: 


Simplifying
(x + 1)(x + 18) = 10

Reorder the terms:
(1 + x)(x + 18) = 10

Reorder the terms:
(1 + x)(18 + x) = 10

Multiply (1 + x) * (18 + x)
(1(18 + x) + x(18 + x)) = 10
((18 * 1 + x * 1) + x(18 + x)) = 10
((18 + 1x) + x(18 + x)) = 10
(18 + 1x + (18 * x + x * x)) = 10
(18 + 1x + (18x + x2)) = 10

Combine like terms: 1x + 18x = 19x
(18 + 19x + x2) = 10

Solving
18 + 19x + x2 = 10

Solving for variable 'x'.

Reorder the terms:
18 + -10 + 19x + x2 = 10 + -10

Combine like terms: 18 + -10 = 8
8 + 19x + x2 = 10 + -10

Combine like terms: 10 + -10 = 0
8 + 19x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + 19x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + 19x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 19x + x2 = 0 + -8
19x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
19x + x2 = -8

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 = -8 + 90.25

Reorder the terms:
90.25 + 19x + x2 = -8 + 90.25

Combine like terms: -8 + 90.25 = 82.25
90.25 + 19x + x2 = 82.25

Factor a perfect square on the left side:
(x + 9.5)(x + 9.5) = 82.25

Calculate the square root of the right side: 9.069178574

Break this problem into two subproblems by setting 
(x + 9.5) equal to 9.069178574 and -9.069178574.


Subproblem 1
x + 9.5 = 9.069178574

Simplifying
x + 9.5 = 9.069178574

Reorder the terms:
9.5 + x = 9.069178574

Solving
9.5 + x = 9.069178574

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 = 9.069178574 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + x = 9.069178574 + -9.5
x = 9.069178574 + -9.5

Combine like terms: 9.069178574 + -9.5 = -0.430821426
x = -0.430821426

Simplifying
x = -0.430821426


Subproblem 2
x + 9.5 = -9.069178574

Simplifying
x + 9.5 = -9.069178574

Reorder the terms:
9.5 + x = -9.069178574

Solving
9.5 + x = -9.069178574

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 = -9.069178574 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + x = -9.069178574 + -9.5
x = -9.069178574 + -9.5

Combine like terms: -9.069178574 + -9.5 = -18.569178574
x = -18.569178574

Simplifying
x = -18.569178574


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.430821426, -18.569178574}

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