3a^2-26a+30=0

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Solution for 3a^2-26a+30=0 equation: 


Simplifying
3a2 + -26a + 30 = 0

Reorder the terms:
30 + -26a + 3a2 = 0

Solving
30 + -26a + 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'.
10 + -8.666666667a + a2 = 0

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -8.666666667a + -10 + a2 = 0 + -10

Reorder the terms:
10 + -10 + -8.666666667a + a2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -8.666666667a + a2 = 0 + -10
-8.666666667a + a2 = 0 + -10

Combine like terms: 0 + -10 = -10
-8.666666667a + a2 = -10

The a term is -8.666666667a.  Take half its coefficient (-4.333333334).
Square it (18.77777778) and add it to both sides.

Add '18.77777778' to each side of the equation.
-8.666666667a + 18.77777778 + a2 = -10 + 18.77777778

Reorder the terms:
18.77777778 + -8.666666667a + a2 = -10 + 18.77777778

Combine like terms: -10 + 18.77777778 = 8.77777778
18.77777778 + -8.666666667a + a2 = 8.77777778

Factor a perfect square on the left side:
(a + -4.333333334)(a + -4.333333334) = 8.77777778

Calculate the square root of the right side: 2.962731473

Break this problem into two subproblems by setting 
(a + -4.333333334) equal to 2.962731473 and -2.962731473.


Subproblem 1
a + -4.333333334 = 2.962731473

Simplifying
a + -4.333333334 = 2.962731473

Reorder the terms:
-4.333333334 + a = 2.962731473

Solving
-4.333333334 + a = 2.962731473

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '4.333333334' to each side of the equation.
-4.333333334 + 4.333333334 + a = 2.962731473 + 4.333333334

Combine like terms: -4.333333334 + 4.333333334 = 0.000000000
0.000000000 + a = 2.962731473 + 4.333333334
a = 2.962731473 + 4.333333334

Combine like terms: 2.962731473 + 4.333333334 = 7.296064807
a = 7.296064807

Simplifying
a = 7.296064807


Subproblem 2
a + -4.333333334 = -2.962731473

Simplifying
a + -4.333333334 = -2.962731473

Reorder the terms:
-4.333333334 + a = -2.962731473

Solving
-4.333333334 + a = -2.962731473

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '4.333333334' to each side of the equation.
-4.333333334 + 4.333333334 + a = -2.962731473 + 4.333333334

Combine like terms: -4.333333334 + 4.333333334 = 0.000000000
0.000000000 + a = -2.962731473 + 4.333333334
a = -2.962731473 + 4.333333334

Combine like terms: -2.962731473 + 4.333333334 = 1.370601861
a = 1.370601861

Simplifying
a = 1.370601861


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {7.296064807, 1.370601861}

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