2a^2-27a+72=0

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Solution for 2a^2-27a+72=0 equation:


Simplifying
2a2 + -27a + 72 = 0

Reorder the terms:
72 + -27a + 2a2 = 0

Solving
72 + -27a + 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'.
36 + -13.5a + a2 = 0

Move the constant term to the right:

Add '-36' to each side of the equation.
36 + -13.5a + -36 + a2 = 0 + -36

Reorder the terms:
36 + -36 + -13.5a + a2 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + -13.5a + a2 = 0 + -36
-13.5a + a2 = 0 + -36

Combine like terms: 0 + -36 = -36
-13.5a + a2 = -36

The a term is -13.5a.  Take half its coefficient (-6.75).
Square it (45.5625) and add it to both sides.

Add '45.5625' to each side of the equation.
-13.5a + 45.5625 + a2 = -36 + 45.5625

Reorder the terms:
45.5625 + -13.5a + a2 = -36 + 45.5625

Combine like terms: -36 + 45.5625 = 9.5625
45.5625 + -13.5a + a2 = 9.5625

Factor a perfect square on the left side:
(a + -6.75)(a + -6.75) = 9.5625

Calculate the square root of the right side: 3.092329219

Break this problem into two subproblems by setting 
(a + -6.75) equal to 3.092329219 and -3.092329219.

Subproblem 1

a + -6.75 = 3.092329219 Simplifying a + -6.75 = 3.092329219 Reorder the terms: -6.75 + a = 3.092329219 Solving -6.75 + a = 3.092329219 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6.75' to each side of the equation. -6.75 + 6.75 + a = 3.092329219 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + a = 3.092329219 + 6.75 a = 3.092329219 + 6.75 Combine like terms: 3.092329219 + 6.75 = 9.842329219 a = 9.842329219 Simplifying a = 9.842329219

Subproblem 2

a + -6.75 = -3.092329219 Simplifying a + -6.75 = -3.092329219 Reorder the terms: -6.75 + a = -3.092329219 Solving -6.75 + a = -3.092329219 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6.75' to each side of the equation. -6.75 + 6.75 + a = -3.092329219 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + a = -3.092329219 + 6.75 a = -3.092329219 + 6.75 Combine like terms: -3.092329219 + 6.75 = 3.657670781 a = 3.657670781 Simplifying a = 3.657670781

Solution

The solution to the problem is based on the solutions from the subproblems. a = {9.842329219, 3.657670781}

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