a(a-5)=15

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Solution for a(a-5)=15 equation: 


Simplifying
a(a + -5) = 15

Reorder the terms:
a(-5 + a) = 15
(-5 * a + a * a) = 15
(-5a + a2) = 15

Solving
-5a + a2 = 15

Solving for variable 'a'.

Reorder the terms:
-15 + -5a + a2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + -5a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -5a + 15 + a2 = 0 + 15

Reorder the terms:
-15 + 15 + -5a + a2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -5a + a2 = 0 + 15
-5a + a2 = 0 + 15

Combine like terms: 0 + 15 = 15
-5a + a2 = 15

The a term is -5a.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5a + 6.25 + a2 = 15 + 6.25

Reorder the terms:
6.25 + -5a + a2 = 15 + 6.25

Combine like terms: 15 + 6.25 = 21.25
6.25 + -5a + a2 = 21.25

Factor a perfect square on the left side:
(a + -2.5)(a + -2.5) = 21.25

Calculate the square root of the right side: 4.609772229

Break this problem into two subproblems by setting 
(a + -2.5) equal to 4.609772229 and -4.609772229.


Subproblem 1
a + -2.5 = 4.609772229

Simplifying
a + -2.5 = 4.609772229

Reorder the terms:
-2.5 + a = 4.609772229

Solving
-2.5 + a = 4.609772229

Solving for variable 'a'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + a = 4.609772229 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + a = 4.609772229 + 2.5
a = 4.609772229 + 2.5

Combine like terms: 4.609772229 + 2.5 = 7.109772229
a = 7.109772229

Simplifying
a = 7.109772229


Subproblem 2
a + -2.5 = -4.609772229

Simplifying
a + -2.5 = -4.609772229

Reorder the terms:
-2.5 + a = -4.609772229

Solving
-2.5 + a = -4.609772229

Solving for variable 'a'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + a = -4.609772229 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + a = -4.609772229 + 2.5
a = -4.609772229 + 2.5

Combine like terms: -4.609772229 + 2.5 = -2.109772229
a = -2.109772229

Simplifying
a = -2.109772229


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {7.109772229, -2.109772229}

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