(a+10)2a+44=180

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Solution for (a+10)2a+44=180 equation: 


Simplifying
(a + 10) * 2a + 44 = 180

Reorder the terms:
(10 + a) * 2a + 44 = 180

Reorder the terms for easier multiplication:
2a(10 + a) + 44 = 180
(10 * 2a + a * 2a) + 44 = 180
(20a + 2a2) + 44 = 180

Reorder the terms:
44 + 20a + 2a2 = 180

Solving
44 + 20a + 2a2 = 180

Solving for variable 'a'.

Reorder the terms:
44 + -180 + 20a + 2a2 = 180 + -180

Combine like terms: 44 + -180 = -136
-136 + 20a + 2a2 = 180 + -180

Combine like terms: 180 + -180 = 0
-136 + 20a + 2a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-68 + 10a + a2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-68 + 10a + a2)' equal to zero and attempt to solve:

Simplifying
-68 + 10a + a2 = 0

Solving
-68 + 10a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '68' to each side of the equation.
-68 + 10a + 68 + a2 = 0 + 68

Reorder the terms:
-68 + 68 + 10a + a2 = 0 + 68

Combine like terms: -68 + 68 = 0
0 + 10a + a2 = 0 + 68
10a + a2 = 0 + 68

Combine like terms: 0 + 68 = 68
10a + a2 = 68

The a term is 10a.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10a + 25 + a2 = 68 + 25

Reorder the terms:
25 + 10a + a2 = 68 + 25

Combine like terms: 68 + 25 = 93
25 + 10a + a2 = 93

Factor a perfect square on the left side:
(a + 5)(a + 5) = 93

Calculate the square root of the right side: 9.643650761

Break this problem into two subproblems by setting 
(a + 5) equal to 9.643650761 and -9.643650761.


Subproblem 1
a + 5 = 9.643650761

Simplifying
a + 5 = 9.643650761

Reorder the terms:
5 + a = 9.643650761

Solving
5 + a = 9.643650761

Solving for variable 'a'.

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

Add '-5' to each side of the equation.
5 + -5 + a = 9.643650761 + -5

Combine like terms: 5 + -5 = 0
0 + a = 9.643650761 + -5
a = 9.643650761 + -5

Combine like terms: 9.643650761 + -5 = 4.643650761
a = 4.643650761

Simplifying
a = 4.643650761


Subproblem 2
a + 5 = -9.643650761

Simplifying
a + 5 = -9.643650761

Reorder the terms:
5 + a = -9.643650761

Solving
5 + a = -9.643650761

Solving for variable 'a'.

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

Add '-5' to each side of the equation.
5 + -5 + a = -9.643650761 + -5

Combine like terms: 5 + -5 = 0
0 + a = -9.643650761 + -5
a = -9.643650761 + -5

Combine like terms: -9.643650761 + -5 = -14.643650761
a = -14.643650761

Simplifying
a = -14.643650761


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {4.643650761, -14.643650761}
Solution
a = {4.643650761, -14.643650761}

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