2a^2-18a-27=0

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Solution for 2a^2-18a-27=0 equation:


Simplifying
2a2 + -18a + -27 = 0

Reorder the terms:
-27 + -18a + 2a2 = 0

Solving
-27 + -18a + 2a2 = 0

Solving for variable 'a'.

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

Divide each side by '2'.
-13.5 + -9a + a2 = 0

Move the constant term to the right:

Add '13.5' to each side of the equation.
-13.5 + -9a + 13.5 + a2 = 0 + 13.5

Reorder the terms:
-13.5 + 13.5 + -9a + a2 = 0 + 13.5

Combine like terms: -13.5 + 13.5 = 0.0
0.0 + -9a + a2 = 0 + 13.5
-9a + a2 = 0 + 13.5

Combine like terms: 0 + 13.5 = 13.5
-9a + a2 = 13.5

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 = 13.5 + 20.25

Reorder the terms:
20.25 + -9a + a2 = 13.5 + 20.25

Combine like terms: 13.5 + 20.25 = 33.75
20.25 + -9a + a2 = 33.75

Factor a perfect square on the left side:
(a + -4.5)(a + -4.5) = 33.75

Calculate the square root of the right side: 5.809475019

Break this problem into two subproblems by setting 
(a + -4.5) equal to 5.809475019 and -5.809475019.

Subproblem 1

a + -4.5 = 5.809475019 Simplifying a + -4.5 = 5.809475019 Reorder the terms: -4.5 + a = 5.809475019 Solving -4.5 + a = 5.809475019 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 = 5.809475019 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + a = 5.809475019 + 4.5 a = 5.809475019 + 4.5 Combine like terms: 5.809475019 + 4.5 = 10.309475019 a = 10.309475019 Simplifying a = 10.309475019

Subproblem 2

a + -4.5 = -5.809475019 Simplifying a + -4.5 = -5.809475019 Reorder the terms: -4.5 + a = -5.809475019 Solving -4.5 + a = -5.809475019 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 = -5.809475019 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + a = -5.809475019 + 4.5 a = -5.809475019 + 4.5 Combine like terms: -5.809475019 + 4.5 = -1.309475019 a = -1.309475019 Simplifying a = -1.309475019

Solution

The solution to the problem is based on the solutions from the subproblems. a = {10.309475019, -1.309475019}

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