(X+6)2X+90=180

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Solution for (X+6)2X+90=180 equation: 


Simplifying
(X + 6) * 2X + 90 = 180

Reorder the terms:
(6 + X) * 2X + 90 = 180

Reorder the terms for easier multiplication:
2X(6 + X) + 90 = 180
(6 * 2X + X * 2X) + 90 = 180
(12X + 2X2) + 90 = 180

Reorder the terms:
90 + 12X + 2X2 = 180

Solving
90 + 12X + 2X2 = 180

Solving for variable 'X'.

Reorder the terms:
90 + -180 + 12X + 2X2 = 180 + -180

Combine like terms: 90 + -180 = -90
-90 + 12X + 2X2 = 180 + -180

Combine like terms: 180 + -180 = 0
-90 + 12X + 2X2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-45 + 6X + X2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-45 + 6X + X2)' equal to zero and attempt to solve:

Simplifying
-45 + 6X + X2 = 0

Solving
-45 + 6X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + 6X + 45 + X2 = 0 + 45

Reorder the terms:
-45 + 45 + 6X + X2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + 6X + X2 = 0 + 45
6X + X2 = 0 + 45

Combine like terms: 0 + 45 = 45
6X + X2 = 45

The X term is 6X.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6X + 9 + X2 = 45 + 9

Reorder the terms:
9 + 6X + X2 = 45 + 9

Combine like terms: 45 + 9 = 54
9 + 6X + X2 = 54

Factor a perfect square on the left side:
(X + 3)(X + 3) = 54

Calculate the square root of the right side: 7.348469228

Break this problem into two subproblems by setting 
(X + 3) equal to 7.348469228 and -7.348469228.


Subproblem 1
X + 3 = 7.348469228

Simplifying
X + 3 = 7.348469228

Reorder the terms:
3 + X = 7.348469228

Solving
3 + X = 7.348469228

Solving for variable 'X'.

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

Add '-3' to each side of the equation.
3 + -3 + X = 7.348469228 + -3

Combine like terms: 3 + -3 = 0
0 + X = 7.348469228 + -3
X = 7.348469228 + -3

Combine like terms: 7.348469228 + -3 = 4.348469228
X = 4.348469228

Simplifying
X = 4.348469228


Subproblem 2
X + 3 = -7.348469228

Simplifying
X + 3 = -7.348469228

Reorder the terms:
3 + X = -7.348469228

Solving
3 + X = -7.348469228

Solving for variable 'X'.

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

Add '-3' to each side of the equation.
3 + -3 + X = -7.348469228 + -3

Combine like terms: 3 + -3 = 0
0 + X = -7.348469228 + -3
X = -7.348469228 + -3

Combine like terms: -7.348469228 + -3 = -10.348469228
X = -10.348469228

Simplifying
X = -10.348469228


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {4.348469228, -10.348469228}
Solution
X = {4.348469228, -10.348469228}

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