8a^2+9a-1=0

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Solution for 8a^2+9a-1=0 equation:


Simplifying
8a2 + 9a + -1 = 0

Reorder the terms:
-1 + 9a + 8a2 = 0

Solving
-1 + 9a + 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'.
-0.125 + 1.125a + a2 = 0

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + 1.125a + 0.125 + a2 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + 1.125a + a2 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + 1.125a + a2 = 0 + 0.125
1.125a + a2 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
1.125a + a2 = 0.125

The a term is 1.125a.  Take half its coefficient (0.5625).
Square it (0.31640625) and add it to both sides.

Add '0.31640625' to each side of the equation.
1.125a + 0.31640625 + a2 = 0.125 + 0.31640625

Reorder the terms:
0.31640625 + 1.125a + a2 = 0.125 + 0.31640625

Combine like terms: 0.125 + 0.31640625 = 0.44140625
0.31640625 + 1.125a + a2 = 0.44140625

Factor a perfect square on the left side:
(a + 0.5625)(a + 0.5625) = 0.44140625

Calculate the square root of the right side: 0.664384113

Break this problem into two subproblems by setting 
(a + 0.5625) equal to 0.664384113 and -0.664384113.

Subproblem 1

a + 0.5625 = 0.664384113 Simplifying a + 0.5625 = 0.664384113 Reorder the terms: 0.5625 + a = 0.664384113 Solving 0.5625 + a = 0.664384113 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + a = 0.664384113 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + a = 0.664384113 + -0.5625 a = 0.664384113 + -0.5625 Combine like terms: 0.664384113 + -0.5625 = 0.101884113 a = 0.101884113 Simplifying a = 0.101884113

Subproblem 2

a + 0.5625 = -0.664384113 Simplifying a + 0.5625 = -0.664384113 Reorder the terms: 0.5625 + a = -0.664384113 Solving 0.5625 + a = -0.664384113 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + a = -0.664384113 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + a = -0.664384113 + -0.5625 a = -0.664384113 + -0.5625 Combine like terms: -0.664384113 + -0.5625 = -1.226884113 a = -1.226884113 Simplifying a = -1.226884113

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.101884113, -1.226884113}

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