a^2-15a+12=0

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Solution for a^2-15a+12=0 equation: 


Simplifying
a2 + -15a + 12 = 0

Reorder the terms:
12 + -15a + a2 = 0

Solving
12 + -15a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + -15a + -12 + a2 = 0 + -12

Reorder the terms:
12 + -12 + -15a + a2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -15a + a2 = 0 + -12
-15a + a2 = 0 + -12

Combine like terms: 0 + -12 = -12
-15a + a2 = -12

The a term is -15a.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15a + 56.25 + a2 = -12 + 56.25

Reorder the terms:
56.25 + -15a + a2 = -12 + 56.25

Combine like terms: -12 + 56.25 = 44.25
56.25 + -15a + a2 = 44.25

Factor a perfect square on the left side:
(a + -7.5)(a + -7.5) = 44.25

Calculate the square root of the right side: 6.652067348

Break this problem into two subproblems by setting 
(a + -7.5) equal to 6.652067348 and -6.652067348.


Subproblem 1
a + -7.5 = 6.652067348

Simplifying
a + -7.5 = 6.652067348

Reorder the terms:
-7.5 + a = 6.652067348

Solving
-7.5 + a = 6.652067348

Solving for variable 'a'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + a = 6.652067348 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + a = 6.652067348 + 7.5
a = 6.652067348 + 7.5

Combine like terms: 6.652067348 + 7.5 = 14.152067348
a = 14.152067348

Simplifying
a = 14.152067348


Subproblem 2
a + -7.5 = -6.652067348

Simplifying
a + -7.5 = -6.652067348

Reorder the terms:
-7.5 + a = -6.652067348

Solving
-7.5 + a = -6.652067348

Solving for variable 'a'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + a = -6.652067348 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + a = -6.652067348 + 7.5
a = -6.652067348 + 7.5

Combine like terms: -6.652067348 + 7.5 = 0.847932652
a = 0.847932652

Simplifying
a = 0.847932652


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {14.152067348, 0.847932652}

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