3a^2-18a+5=0

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Solution for 3a^2-18a+5=0 equation:


Simplifying
3a2 + -18a + 5 = 0

Reorder the terms:
5 + -18a + 3a2 = 0

Solving
5 + -18a + 3a2 = 0

Solving for variable 'a'.

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

Divide each side by '3'.
1.666666667 + -6a + a2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + -6a + -1.666666667 + a2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + -6a + a2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + -6a + a2 = 0 + -1.666666667
-6a + a2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
-6a + a2 = -1.666666667

The a term is -6a.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6a + 9 + a2 = -1.666666667 + 9

Reorder the terms:
9 + -6a + a2 = -1.666666667 + 9

Combine like terms: -1.666666667 + 9 = 7.333333333
9 + -6a + a2 = 7.333333333

Factor a perfect square on the left side:
(a + -3)(a + -3) = 7.333333333

Calculate the square root of the right side: 2.708012801

Break this problem into two subproblems by setting 
(a + -3) equal to 2.708012801 and -2.708012801.

Subproblem 1

a + -3 = 2.708012801 Simplifying a + -3 = 2.708012801 Reorder the terms: -3 + a = 2.708012801 Solving -3 + a = 2.708012801 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + a = 2.708012801 + 3 Combine like terms: -3 + 3 = 0 0 + a = 2.708012801 + 3 a = 2.708012801 + 3 Combine like terms: 2.708012801 + 3 = 5.708012801 a = 5.708012801 Simplifying a = 5.708012801

Subproblem 2

a + -3 = -2.708012801 Simplifying a + -3 = -2.708012801 Reorder the terms: -3 + a = -2.708012801 Solving -3 + a = -2.708012801 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + a = -2.708012801 + 3 Combine like terms: -3 + 3 = 0 0 + a = -2.708012801 + 3 a = -2.708012801 + 3 Combine like terms: -2.708012801 + 3 = 0.291987199 a = 0.291987199 Simplifying a = 0.291987199

Solution

The solution to the problem is based on the solutions from the subproblems. a = {5.708012801, 0.291987199}

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