20a^2-13a-12=0

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Solution for 20a^2-13a-12=0 equation:


Simplifying
20a2 + -13a + -12 = 0

Reorder the terms:
-12 + -13a + 20a2 = 0

Solving
-12 + -13a + 20a2 = 0

Solving for variable 'a'.

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

Divide each side by '20'.
-0.6 + -0.65a + a2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + -0.65a + 0.6 + a2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + -0.65a + a2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + -0.65a + a2 = 0 + 0.6
-0.65a + a2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
-0.65a + a2 = 0.6

The a term is -0.65a.  Take half its coefficient (-0.325).
Square it (0.105625) and add it to both sides.

Add '0.105625' to each side of the equation.
-0.65a + 0.105625 + a2 = 0.6 + 0.105625

Reorder the terms:
0.105625 + -0.65a + a2 = 0.6 + 0.105625

Combine like terms: 0.6 + 0.105625 = 0.705625
0.105625 + -0.65a + a2 = 0.705625

Factor a perfect square on the left side:
(a + -0.325)(a + -0.325) = 0.705625

Calculate the square root of the right side: 0.840014881

Break this problem into two subproblems by setting 
(a + -0.325) equal to 0.840014881 and -0.840014881.

Subproblem 1

a + -0.325 = 0.840014881 Simplifying a + -0.325 = 0.840014881 Reorder the terms: -0.325 + a = 0.840014881 Solving -0.325 + a = 0.840014881 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.325' to each side of the equation. -0.325 + 0.325 + a = 0.840014881 + 0.325 Combine like terms: -0.325 + 0.325 = 0.000 0.000 + a = 0.840014881 + 0.325 a = 0.840014881 + 0.325 Combine like terms: 0.840014881 + 0.325 = 1.165014881 a = 1.165014881 Simplifying a = 1.165014881

Subproblem 2

a + -0.325 = -0.840014881 Simplifying a + -0.325 = -0.840014881 Reorder the terms: -0.325 + a = -0.840014881 Solving -0.325 + a = -0.840014881 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.325' to each side of the equation. -0.325 + 0.325 + a = -0.840014881 + 0.325 Combine like terms: -0.325 + 0.325 = 0.000 0.000 + a = -0.840014881 + 0.325 a = -0.840014881 + 0.325 Combine like terms: -0.840014881 + 0.325 = -0.515014881 a = -0.515014881 Simplifying a = -0.515014881

Solution

The solution to the problem is based on the solutions from the subproblems. a = {1.165014881, -0.515014881}

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