a+36-a^2=0

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Solution for a+36-a^2=0 equation:


Simplifying
a + 36 + -1a2 = 0

Reorder the terms:
36 + a + -1a2 = 0

Solving
36 + a + -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'.
-36 + -1a + a2 = 0

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -1a + 36 + a2 = 0 + 36

Reorder the terms:
-36 + 36 + -1a + a2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -1a + a2 = 0 + 36
-1a + a2 = 0 + 36

Combine like terms: 0 + 36 = 36
-1a + a2 = 36

The a term is a.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1a + 0.25 + a2 = 36 + 0.25

Reorder the terms:
0.25 + -1a + a2 = 36 + 0.25

Combine like terms: 36 + 0.25 = 36.25
0.25 + -1a + a2 = 36.25

Factor a perfect square on the left side:
(a + 0.5)(a + 0.5) = 36.25

Calculate the square root of the right side: 6.020797289

Break this problem into two subproblems by setting 
(a + 0.5) equal to 6.020797289 and -6.020797289.

Subproblem 1

a + 0.5 = 6.020797289 Simplifying a + 0.5 = 6.020797289 Reorder the terms: 0.5 + a = 6.020797289 Solving 0.5 + a = 6.020797289 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = 6.020797289 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = 6.020797289 + -0.5 a = 6.020797289 + -0.5 Combine like terms: 6.020797289 + -0.5 = 5.520797289 a = 5.520797289 Simplifying a = 5.520797289

Subproblem 2

a + 0.5 = -6.020797289 Simplifying a + 0.5 = -6.020797289 Reorder the terms: 0.5 + a = -6.020797289 Solving 0.5 + a = -6.020797289 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = -6.020797289 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = -6.020797289 + -0.5 a = -6.020797289 + -0.5 Combine like terms: -6.020797289 + -0.5 = -6.520797289 a = -6.520797289 Simplifying a = -6.520797289

Solution

The solution to the problem is based on the solutions from the subproblems. a = {5.520797289, -6.520797289}

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