9a=a^2-18

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Solution for 9a=a^2-18 equation:


Simplifying
9a = a2 + -18

Reorder the terms:
9a = -18 + a2

Solving
9a = -18 + a2

Solving for variable 'a'.

Reorder the terms:
18 + 9a + -1a2 = -18 + a2 + 18 + -1a2

Reorder the terms:
18 + 9a + -1a2 = -18 + 18 + a2 + -1a2

Combine like terms: -18 + 18 = 0
18 + 9a + -1a2 = 0 + a2 + -1a2
18 + 9a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
18 + 9a + -1a2 = 0

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

Divide each side by '-1'.
-18 + -9a + a2 = 0

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + -9a + 18 + a2 = 0 + 18

Reorder the terms:
-18 + 18 + -9a + a2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -9a + a2 = 0 + 18
-9a + a2 = 0 + 18

Combine like terms: 0 + 18 = 18
-9a + a2 = 18

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 = 18 + 20.25

Reorder the terms:
20.25 + -9a + a2 = 18 + 20.25

Combine like terms: 18 + 20.25 = 38.25
20.25 + -9a + a2 = 38.25

Factor a perfect square on the left side:
(a + -4.5)(a + -4.5) = 38.25

Calculate the square root of the right side: 6.184658438

Break this problem into two subproblems by setting 
(a + -4.5) equal to 6.184658438 and -6.184658438.

Subproblem 1

a + -4.5 = 6.184658438 Simplifying a + -4.5 = 6.184658438 Reorder the terms: -4.5 + a = 6.184658438 Solving -4.5 + a = 6.184658438 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 = 6.184658438 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + a = 6.184658438 + 4.5 a = 6.184658438 + 4.5 Combine like terms: 6.184658438 + 4.5 = 10.684658438 a = 10.684658438 Simplifying a = 10.684658438

Subproblem 2

a + -4.5 = -6.184658438 Simplifying a + -4.5 = -6.184658438 Reorder the terms: -4.5 + a = -6.184658438 Solving -4.5 + a = -6.184658438 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 = -6.184658438 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + a = -6.184658438 + 4.5 a = -6.184658438 + 4.5 Combine like terms: -6.184658438 + 4.5 = -1.684658438 a = -1.684658438 Simplifying a = -1.684658438

Solution

The solution to the problem is based on the solutions from the subproblems. a = {10.684658438, -1.684658438}

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