2a^2-18a+9=0

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Solution for 2a^2-18a+9=0 equation:


Simplifying
2a2 + -18a + 9 = 0

Reorder the terms:
9 + -18a + 2a2 = 0

Solving
9 + -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'.
4.5 + -9a + a2 = 0

Move the constant term to the right:

Add '-4.5' to each side of the equation.
4.5 + -9a + -4.5 + a2 = 0 + -4.5

Reorder the terms:
4.5 + -4.5 + -9a + a2 = 0 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + -9a + a2 = 0 + -4.5
-9a + a2 = 0 + -4.5

Combine like terms: 0 + -4.5 = -4.5
-9a + a2 = -4.5

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 = -4.5 + 20.25

Reorder the terms:
20.25 + -9a + a2 = -4.5 + 20.25

Combine like terms: -4.5 + 20.25 = 15.75
20.25 + -9a + a2 = 15.75

Factor a perfect square on the left side:
(a + -4.5)(a + -4.5) = 15.75

Calculate the square root of the right side: 3.968626967

Break this problem into two subproblems by setting 
(a + -4.5) equal to 3.968626967 and -3.968626967.

Subproblem 1

a + -4.5 = 3.968626967 Simplifying a + -4.5 = 3.968626967 Reorder the terms: -4.5 + a = 3.968626967 Solving -4.5 + a = 3.968626967 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 = 3.968626967 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + a = 3.968626967 + 4.5 a = 3.968626967 + 4.5 Combine like terms: 3.968626967 + 4.5 = 8.468626967 a = 8.468626967 Simplifying a = 8.468626967

Subproblem 2

a + -4.5 = -3.968626967 Simplifying a + -4.5 = -3.968626967 Reorder the terms: -4.5 + a = -3.968626967 Solving -4.5 + a = -3.968626967 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 = -3.968626967 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + a = -3.968626967 + 4.5 a = -3.968626967 + 4.5 Combine like terms: -3.968626967 + 4.5 = 0.531373033 a = 0.531373033 Simplifying a = 0.531373033

Solution

The solution to the problem is based on the solutions from the subproblems. a = {8.468626967, 0.531373033}

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