6a(1+8)a=9a+1

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Solution for 6a(1+8)a=9a+1 equation:


Simplifying
6a(1 + 8) * a = 9a + 1

Combine like terms: 1 + 8 = 9
6a(9) * a = 9a + 1

Reorder the terms for easier multiplication:
6 * 9a * a = 9a + 1

Multiply 6 * 9
54a * a = 9a + 1

Multiply a * a
54a2 = 9a + 1

Reorder the terms:
54a2 = 1 + 9a

Solving
54a2 = 1 + 9a

Solving for variable 'a'.

Reorder the terms:
-1 + -9a + 54a2 = 1 + 9a + -1 + -9a

Reorder the terms:
-1 + -9a + 54a2 = 1 + -1 + 9a + -9a

Combine like terms: 1 + -1 = 0
-1 + -9a + 54a2 = 0 + 9a + -9a
-1 + -9a + 54a2 = 9a + -9a

Combine like terms: 9a + -9a = 0
-1 + -9a + 54a2 = 0

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

Divide each side by '54'.
-0.01851851852 + -0.1666666667a + a2 = 0

Move the constant term to the right:

Add '0.01851851852' to each side of the equation.
-0.01851851852 + -0.1666666667a + 0.01851851852 + a2 = 0 + 0.01851851852

Reorder the terms:
-0.01851851852 + 0.01851851852 + -0.1666666667a + a2 = 0 + 0.01851851852

Combine like terms: -0.01851851852 + 0.01851851852 = 0.00000000000
0.00000000000 + -0.1666666667a + a2 = 0 + 0.01851851852
-0.1666666667a + a2 = 0 + 0.01851851852

Combine like terms: 0 + 0.01851851852 = 0.01851851852
-0.1666666667a + a2 = 0.01851851852

The a term is -0.1666666667a.  Take half its coefficient (-0.08333333335).
Square it (0.006944444447) and add it to both sides.

Add '0.006944444447' to each side of the equation.
-0.1666666667a + 0.006944444447 + a2 = 0.01851851852 + 0.006944444447

Reorder the terms:
0.006944444447 + -0.1666666667a + a2 = 0.01851851852 + 0.006944444447

Combine like terms: 0.01851851852 + 0.006944444447 = 0.025462962967
0.006944444447 + -0.1666666667a + a2 = 0.025462962967

Factor a perfect square on the left side:
(a + -0.08333333335)(a + -0.08333333335) = 0.025462962967

Calculate the square root of the right side: 0.159571185

Break this problem into two subproblems by setting 
(a + -0.08333333335) equal to 0.159571185 and -0.159571185.

Subproblem 1

a + -0.08333333335 = 0.159571185 Simplifying a + -0.08333333335 = 0.159571185 Reorder the terms: -0.08333333335 + a = 0.159571185 Solving -0.08333333335 + a = 0.159571185 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + a = 0.159571185 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + a = 0.159571185 + 0.08333333335 a = 0.159571185 + 0.08333333335 Combine like terms: 0.159571185 + 0.08333333335 = 0.24290451835 a = 0.24290451835 Simplifying a = 0.24290451835

Subproblem 2

a + -0.08333333335 = -0.159571185 Simplifying a + -0.08333333335 = -0.159571185 Reorder the terms: -0.08333333335 + a = -0.159571185 Solving -0.08333333335 + a = -0.159571185 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + a = -0.159571185 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + a = -0.159571185 + 0.08333333335 a = -0.159571185 + 0.08333333335 Combine like terms: -0.159571185 + 0.08333333335 = -0.07623785165 a = -0.07623785165 Simplifying a = -0.07623785165

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.24290451835, -0.07623785165}

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