8a^2-3a-9=0

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Solution for 8a^2-3a-9=0 equation:


Simplifying
8a2 + -3a + -9 = 0

Reorder the terms:
-9 + -3a + 8a2 = 0

Solving
-9 + -3a + 8a2 = 0

Solving for variable 'a'.

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

Divide each side by '8'.
-1.125 + -0.375a + a2 = 0

Move the constant term to the right:

Add '1.125' to each side of the equation.
-1.125 + -0.375a + 1.125 + a2 = 0 + 1.125

Reorder the terms:
-1.125 + 1.125 + -0.375a + a2 = 0 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + -0.375a + a2 = 0 + 1.125
-0.375a + a2 = 0 + 1.125

Combine like terms: 0 + 1.125 = 1.125
-0.375a + a2 = 1.125

The a term is -0.375a.  Take half its coefficient (-0.1875).
Square it (0.03515625) and add it to both sides.

Add '0.03515625' to each side of the equation.
-0.375a + 0.03515625 + a2 = 1.125 + 0.03515625

Reorder the terms:
0.03515625 + -0.375a + a2 = 1.125 + 0.03515625

Combine like terms: 1.125 + 0.03515625 = 1.16015625
0.03515625 + -0.375a + a2 = 1.16015625

Factor a perfect square on the left side:
(a + -0.1875)(a + -0.1875) = 1.16015625

Calculate the square root of the right side: 1.077105496

Break this problem into two subproblems by setting 
(a + -0.1875) equal to 1.077105496 and -1.077105496.

Subproblem 1

a + -0.1875 = 1.077105496 Simplifying a + -0.1875 = 1.077105496 Reorder the terms: -0.1875 + a = 1.077105496 Solving -0.1875 + a = 1.077105496 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + a = 1.077105496 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + a = 1.077105496 + 0.1875 a = 1.077105496 + 0.1875 Combine like terms: 1.077105496 + 0.1875 = 1.264605496 a = 1.264605496 Simplifying a = 1.264605496

Subproblem 2

a + -0.1875 = -1.077105496 Simplifying a + -0.1875 = -1.077105496 Reorder the terms: -0.1875 + a = -1.077105496 Solving -0.1875 + a = -1.077105496 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + a = -1.077105496 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + a = -1.077105496 + 0.1875 a = -1.077105496 + 0.1875 Combine like terms: -1.077105496 + 0.1875 = -0.889605496 a = -0.889605496 Simplifying a = -0.889605496

Solution

The solution to the problem is based on the solutions from the subproblems. a = {1.264605496, -0.889605496}

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