3a(25+a)=225

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Solution for 3a(25+a)=225 equation: 


Simplifying
3a(25 + a) = 225
(25 * 3a + a * 3a) = 225
(75a + 3a2) = 225

Solving
75a + 3a2 = 225

Solving for variable 'a'.

Reorder the terms:
-225 + 75a + 3a2 = 225 + -225

Combine like terms: 225 + -225 = 0
-225 + 75a + 3a2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-75 + 25a + a2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-75 + 25a + a2)' equal to zero and attempt to solve:

Simplifying
-75 + 25a + a2 = 0

Solving
-75 + 25a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '75' to each side of the equation.
-75 + 25a + 75 + a2 = 0 + 75

Reorder the terms:
-75 + 75 + 25a + a2 = 0 + 75

Combine like terms: -75 + 75 = 0
0 + 25a + a2 = 0 + 75
25a + a2 = 0 + 75

Combine like terms: 0 + 75 = 75
25a + a2 = 75

The a term is 25a.  Take half its coefficient (12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
25a + 156.25 + a2 = 75 + 156.25

Reorder the terms:
156.25 + 25a + a2 = 75 + 156.25

Combine like terms: 75 + 156.25 = 231.25
156.25 + 25a + a2 = 231.25

Factor a perfect square on the left side:
(a + 12.5)(a + 12.5) = 231.25

Calculate the square root of the right side: 15.206906326

Break this problem into two subproblems by setting 
(a + 12.5) equal to 15.206906326 and -15.206906326.


Subproblem 1
a + 12.5 = 15.206906326

Simplifying
a + 12.5 = 15.206906326

Reorder the terms:
12.5 + a = 15.206906326

Solving
12.5 + a = 15.206906326

Solving for variable 'a'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + a = 15.206906326 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + a = 15.206906326 + -12.5
a = 15.206906326 + -12.5

Combine like terms: 15.206906326 + -12.5 = 2.706906326
a = 2.706906326

Simplifying
a = 2.706906326


Subproblem 2
a + 12.5 = -15.206906326

Simplifying
a + 12.5 = -15.206906326

Reorder the terms:
12.5 + a = -15.206906326

Solving
12.5 + a = -15.206906326

Solving for variable 'a'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + a = -15.206906326 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + a = -15.206906326 + -12.5
a = -15.206906326 + -12.5

Combine like terms: -15.206906326 + -12.5 = -27.706906326
a = -27.706906326

Simplifying
a = -27.706906326


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {2.706906326, -27.706906326}
Solution
a = {2.706906326, -27.706906326}

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