2a^2-20a+27=0

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Solution for 2a^2-20a+27=0 equation:


Simplifying
2a2 + -20a + 27 = 0

Reorder the terms:
27 + -20a + 2a2 = 0

Solving
27 + -20a + 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 + -10a + a2 = 0

Move the constant term to the right:

Add '-13.5' to each side of the equation.
13.5 + -10a + -13.5 + a2 = 0 + -13.5

Reorder the terms:
13.5 + -13.5 + -10a + a2 = 0 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + -10a + a2 = 0 + -13.5
-10a + a2 = 0 + -13.5

Combine like terms: 0 + -13.5 = -13.5
-10a + a2 = -13.5

The a term is -10a.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10a + 25 + a2 = -13.5 + 25

Reorder the terms:
25 + -10a + a2 = -13.5 + 25

Combine like terms: -13.5 + 25 = 11.5
25 + -10a + a2 = 11.5

Factor a perfect square on the left side:
(a + -5)(a + -5) = 11.5

Calculate the square root of the right side: 3.391164992

Break this problem into two subproblems by setting 
(a + -5) equal to 3.391164992 and -3.391164992.

Subproblem 1

a + -5 = 3.391164992 Simplifying a + -5 = 3.391164992 Reorder the terms: -5 + a = 3.391164992 Solving -5 + a = 3.391164992 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + a = 3.391164992 + 5 Combine like terms: -5 + 5 = 0 0 + a = 3.391164992 + 5 a = 3.391164992 + 5 Combine like terms: 3.391164992 + 5 = 8.391164992 a = 8.391164992 Simplifying a = 8.391164992

Subproblem 2

a + -5 = -3.391164992 Simplifying a + -5 = -3.391164992 Reorder the terms: -5 + a = -3.391164992 Solving -5 + a = -3.391164992 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + a = -3.391164992 + 5 Combine like terms: -5 + 5 = 0 0 + a = -3.391164992 + 5 a = -3.391164992 + 5 Combine like terms: -3.391164992 + 5 = 1.608835008 a = 1.608835008 Simplifying a = 1.608835008

Solution

The solution to the problem is based on the solutions from the subproblems. a = {8.391164992, 1.608835008}

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