-a^2+20a-60=0

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Solution for -a^2+20a-60=0 equation: 


Simplifying
-1a2 + 20a + -60 = 0

Reorder the terms:
-60 + 20a + -1a2 = 0

Solving
-60 + 20a + -1a2 = 0

Solving for variable 'a'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
60 + -20a + a2 = 0

Move the constant term to the right:

Add '-60' to each side of the equation.
60 + -20a + -60 + a2 = 0 + -60

Reorder the terms:
60 + -60 + -20a + a2 = 0 + -60

Combine like terms: 60 + -60 = 0
0 + -20a + a2 = 0 + -60
-20a + a2 = 0 + -60

Combine like terms: 0 + -60 = -60
-20a + a2 = -60

The a term is -20a.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20a + 100 + a2 = -60 + 100

Reorder the terms:
100 + -20a + a2 = -60 + 100

Combine like terms: -60 + 100 = 40
100 + -20a + a2 = 40

Factor a perfect square on the left side:
(a + -10)(a + -10) = 40

Calculate the square root of the right side: 6.32455532

Break this problem into two subproblems by setting 
(a + -10) equal to 6.32455532 and -6.32455532.


Subproblem 1
a + -10 = 6.32455532

Simplifying
a + -10 = 6.32455532

Reorder the terms:
-10 + a = 6.32455532

Solving
-10 + a = 6.32455532

Solving for variable 'a'.

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

Add '10' to each side of the equation.
-10 + 10 + a = 6.32455532 + 10

Combine like terms: -10 + 10 = 0
0 + a = 6.32455532 + 10
a = 6.32455532 + 10

Combine like terms: 6.32455532 + 10 = 16.32455532
a = 16.32455532

Simplifying
a = 16.32455532


Subproblem 2
a + -10 = -6.32455532

Simplifying
a + -10 = -6.32455532

Reorder the terms:
-10 + a = -6.32455532

Solving
-10 + a = -6.32455532

Solving for variable 'a'.

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

Add '10' to each side of the equation.
-10 + 10 + a = -6.32455532 + 10

Combine like terms: -10 + 10 = 0
0 + a = -6.32455532 + 10
a = -6.32455532 + 10

Combine like terms: -6.32455532 + 10 = 3.67544468
a = 3.67544468

Simplifying
a = 3.67544468


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {16.32455532, 3.67544468}

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