9a^2-5a-12=0

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Solution for 9a^2-5a-12=0 equation:


Simplifying
9a2 + -5a + -12 = 0

Reorder the terms:
-12 + -5a + 9a2 = 0

Solving
-12 + -5a + 9a2 = 0

Solving for variable 'a'.

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

Divide each side by '9'.
-1.333333333 + -0.5555555556a + a2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + -0.5555555556a + 1.333333333 + a2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + -0.5555555556a + a2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + -0.5555555556a + a2 = 0 + 1.333333333
-0.5555555556a + a2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
-0.5555555556a + a2 = 1.333333333

The a term is -0.5555555556a.  Take half its coefficient (-0.2777777778).
Square it (0.07716049384) and add it to both sides.

Add '0.07716049384' to each side of the equation.
-0.5555555556a + 0.07716049384 + a2 = 1.333333333 + 0.07716049384

Reorder the terms:
0.07716049384 + -0.5555555556a + a2 = 1.333333333 + 0.07716049384

Combine like terms: 1.333333333 + 0.07716049384 = 1.41049382684
0.07716049384 + -0.5555555556a + a2 = 1.41049382684

Factor a perfect square on the left side:
(a + -0.2777777778)(a + -0.2777777778) = 1.41049382684

Calculate the square root of the right side: 1.187642129

Break this problem into two subproblems by setting 
(a + -0.2777777778) equal to 1.187642129 and -1.187642129.

Subproblem 1

a + -0.2777777778 = 1.187642129 Simplifying a + -0.2777777778 = 1.187642129 Reorder the terms: -0.2777777778 + a = 1.187642129 Solving -0.2777777778 + a = 1.187642129 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.2777777778 + a = 1.187642129 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + a = 1.187642129 + 0.2777777778 a = 1.187642129 + 0.2777777778 Combine like terms: 1.187642129 + 0.2777777778 = 1.4654199068 a = 1.4654199068 Simplifying a = 1.4654199068

Subproblem 2

a + -0.2777777778 = -1.187642129 Simplifying a + -0.2777777778 = -1.187642129 Reorder the terms: -0.2777777778 + a = -1.187642129 Solving -0.2777777778 + a = -1.187642129 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.2777777778 + a = -1.187642129 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + a = -1.187642129 + 0.2777777778 a = -1.187642129 + 0.2777777778 Combine like terms: -1.187642129 + 0.2777777778 = -0.9098643512 a = -0.9098643512 Simplifying a = -0.9098643512

Solution

The solution to the problem is based on the solutions from the subproblems. a = {1.4654199068, -0.9098643512}

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