9a^2-18a-47=0

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Solution for 9a^2-18a-47=0 equation:


Simplifying
9a2 + -18a + -47 = 0

Reorder the terms:
-47 + -18a + 9a2 = 0

Solving
-47 + -18a + 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'.
-5.222222222 + -2a + a2 = 0

Move the constant term to the right:

Add '5.222222222' to each side of the equation.
-5.222222222 + -2a + 5.222222222 + a2 = 0 + 5.222222222

Reorder the terms:
-5.222222222 + 5.222222222 + -2a + a2 = 0 + 5.222222222

Combine like terms: -5.222222222 + 5.222222222 = 0.000000000
0.000000000 + -2a + a2 = 0 + 5.222222222
-2a + a2 = 0 + 5.222222222

Combine like terms: 0 + 5.222222222 = 5.222222222
-2a + a2 = 5.222222222

The a term is -2a.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2a + 1 + a2 = 5.222222222 + 1

Reorder the terms:
1 + -2a + a2 = 5.222222222 + 1

Combine like terms: 5.222222222 + 1 = 6.222222222
1 + -2a + a2 = 6.222222222

Factor a perfect square on the left side:
(a + -1)(a + -1) = 6.222222222

Calculate the square root of the right side: 2.494438258

Break this problem into two subproblems by setting 
(a + -1) equal to 2.494438258 and -2.494438258.

Subproblem 1

a + -1 = 2.494438258 Simplifying a + -1 = 2.494438258 Reorder the terms: -1 + a = 2.494438258 Solving -1 + a = 2.494438258 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + a = 2.494438258 + 1 Combine like terms: -1 + 1 = 0 0 + a = 2.494438258 + 1 a = 2.494438258 + 1 Combine like terms: 2.494438258 + 1 = 3.494438258 a = 3.494438258 Simplifying a = 3.494438258

Subproblem 2

a + -1 = -2.494438258 Simplifying a + -1 = -2.494438258 Reorder the terms: -1 + a = -2.494438258 Solving -1 + a = -2.494438258 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + a = -2.494438258 + 1 Combine like terms: -1 + 1 = 0 0 + a = -2.494438258 + 1 a = -2.494438258 + 1 Combine like terms: -2.494438258 + 1 = -1.494438258 a = -1.494438258 Simplifying a = -1.494438258

Solution

The solution to the problem is based on the solutions from the subproblems. a = {3.494438258, -1.494438258}

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