(X+2)(X+10)=90

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Solution for (X+2)(X+10)=90 equation: 


Simplifying
(X + 2)(X + 10) = 90

Reorder the terms:
(2 + X)(X + 10) = 90

Reorder the terms:
(2 + X)(10 + X) = 90

Multiply (2 + X) * (10 + X)
(2(10 + X) + X(10 + X)) = 90
((10 * 2 + X * 2) + X(10 + X)) = 90
((20 + 2X) + X(10 + X)) = 90
(20 + 2X + (10 * X + X * X)) = 90
(20 + 2X + (10X + X2)) = 90

Combine like terms: 2X + 10X = 12X
(20 + 12X + X2) = 90

Solving
20 + 12X + X2 = 90

Solving for variable 'X'.

Reorder the terms:
20 + -90 + 12X + X2 = 90 + -90

Combine like terms: 20 + -90 = -70
-70 + 12X + X2 = 90 + -90

Combine like terms: 90 + -90 = 0
-70 + 12X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '70' to each side of the equation.
-70 + 12X + 70 + X2 = 0 + 70

Reorder the terms:
-70 + 70 + 12X + X2 = 0 + 70

Combine like terms: -70 + 70 = 0
0 + 12X + X2 = 0 + 70
12X + X2 = 0 + 70

Combine like terms: 0 + 70 = 70
12X + X2 = 70

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 = 70 + 36

Reorder the terms:
36 + 12X + X2 = 70 + 36

Combine like terms: 70 + 36 = 106
36 + 12X + X2 = 106

Factor a perfect square on the left side:
(X + 6)(X + 6) = 106

Calculate the square root of the right side: 10.295630141

Break this problem into two subproblems by setting 
(X + 6) equal to 10.295630141 and -10.295630141.


Subproblem 1
X + 6 = 10.295630141

Simplifying
X + 6 = 10.295630141

Reorder the terms:
6 + X = 10.295630141

Solving
6 + X = 10.295630141

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 = 10.295630141 + -6

Combine like terms: 6 + -6 = 0
0 + X = 10.295630141 + -6
X = 10.295630141 + -6

Combine like terms: 10.295630141 + -6 = 4.295630141
X = 4.295630141

Simplifying
X = 4.295630141


Subproblem 2
X + 6 = -10.295630141

Simplifying
X + 6 = -10.295630141

Reorder the terms:
6 + X = -10.295630141

Solving
6 + X = -10.295630141

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 = -10.295630141 + -6

Combine like terms: 6 + -6 = 0
0 + X = -10.295630141 + -6
X = -10.295630141 + -6

Combine like terms: -10.295630141 + -6 = -16.295630141
X = -16.295630141

Simplifying
X = -16.295630141


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {4.295630141, -16.295630141}

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