1-6a+54a+3a^2=

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Solution for 1-6a+54a+3a^2= equation:


Simplifying
1 + -6a + 54a + 3a2 = 0

Combine like terms: -6a + 54a = 48a
1 + 48a + 3a2 = 0

Solving
1 + 48a + 3a2 = 0

Solving for variable 'a'.

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

Divide each side by '3'.
0.3333333333 + 16a + a2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + 16a + -0.3333333333 + a2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + 16a + a2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + 16a + a2 = 0 + -0.3333333333
16a + a2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
16a + a2 = -0.3333333333

The a term is 16a.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16a + 64 + a2 = -0.3333333333 + 64

Reorder the terms:
64 + 16a + a2 = -0.3333333333 + 64

Combine like terms: -0.3333333333 + 64 = 63.6666666667
64 + 16a + a2 = 63.6666666667

Factor a perfect square on the left side:
(a + 8)(a + 8) = 63.6666666667

Calculate the square root of the right side: 7.979139469

Break this problem into two subproblems by setting 
(a + 8) equal to 7.979139469 and -7.979139469.

Subproblem 1

a + 8 = 7.979139469 Simplifying a + 8 = 7.979139469 Reorder the terms: 8 + a = 7.979139469 Solving 8 + a = 7.979139469 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + a = 7.979139469 + -8 Combine like terms: 8 + -8 = 0 0 + a = 7.979139469 + -8 a = 7.979139469 + -8 Combine like terms: 7.979139469 + -8 = -0.020860531 a = -0.020860531 Simplifying a = -0.020860531

Subproblem 2

a + 8 = -7.979139469 Simplifying a + 8 = -7.979139469 Reorder the terms: 8 + a = -7.979139469 Solving 8 + a = -7.979139469 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + a = -7.979139469 + -8 Combine like terms: 8 + -8 = 0 0 + a = -7.979139469 + -8 a = -7.979139469 + -8 Combine like terms: -7.979139469 + -8 = -15.979139469 a = -15.979139469 Simplifying a = -15.979139469

Solution

The solution to the problem is based on the solutions from the subproblems. a = {-0.020860531, -15.979139469}

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