a^2+9a+20.25=682

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Solution for a^2+9a+20.25=682 equation: 


Simplifying
a2 + 9a + 20.25 = 682

Reorder the terms:
20.25 + 9a + a2 = 682

Solving
20.25 + 9a + a2 = 682

Solving for variable 'a'.

Reorder the terms:
20.25 + -682 + 9a + a2 = 682 + -682

Combine like terms: 20.25 + -682 = -661.75
-661.75 + 9a + a2 = 682 + -682

Combine like terms: 682 + -682 = 0
-661.75 + 9a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '661.75' to each side of the equation.
-661.75 + 9a + 661.75 + a2 = 0 + 661.75

Reorder the terms:
-661.75 + 661.75 + 9a + a2 = 0 + 661.75

Combine like terms: -661.75 + 661.75 = 0.00
0.00 + 9a + a2 = 0 + 661.75
9a + a2 = 0 + 661.75

Combine like terms: 0 + 661.75 = 661.75
9a + a2 = 661.75

The a term is 9a.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9a + 20.25 + a2 = 661.75 + 20.25

Reorder the terms:
20.25 + 9a + a2 = 661.75 + 20.25

Combine like terms: 661.75 + 20.25 = 682
20.25 + 9a + a2 = 682

Factor a perfect square on the left side:
(a + 4.5)(a + 4.5) = 682

Calculate the square root of the right side: 26.115129714

Break this problem into two subproblems by setting 
(a + 4.5) equal to 26.115129714 and -26.115129714.


Subproblem 1
a + 4.5 = 26.115129714

Simplifying
a + 4.5 = 26.115129714

Reorder the terms:
4.5 + a = 26.115129714

Solving
4.5 + a = 26.115129714

Solving for variable 'a'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + a = 26.115129714 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + a = 26.115129714 + -4.5
a = 26.115129714 + -4.5

Combine like terms: 26.115129714 + -4.5 = 21.615129714
a = 21.615129714

Simplifying
a = 21.615129714


Subproblem 2
a + 4.5 = -26.115129714

Simplifying
a + 4.5 = -26.115129714

Reorder the terms:
4.5 + a = -26.115129714

Solving
4.5 + a = -26.115129714

Solving for variable 'a'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + a = -26.115129714 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + a = -26.115129714 + -4.5
a = -26.115129714 + -4.5

Combine like terms: -26.115129714 + -4.5 = -30.615129714
a = -30.615129714

Simplifying
a = -30.615129714


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {21.615129714, -30.615129714}

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