3a^2-6a=34

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Solution for 3a^2-6a=34 equation:


Simplifying
3a2 + -6a = 34

Reorder the terms:
-6a + 3a2 = 34

Solving
-6a + 3a2 = 34

Solving for variable 'a'.

Reorder the terms:
-34 + -6a + 3a2 = 34 + -34

Combine like terms: 34 + -34 = 0
-34 + -6a + 3a2 = 0

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

Divide each side by '3'.
-11.33333333 + -2a + a2 = 0

Move the constant term to the right:

Add '11.33333333' to each side of the equation.
-11.33333333 + -2a + 11.33333333 + a2 = 0 + 11.33333333

Reorder the terms:
-11.33333333 + 11.33333333 + -2a + a2 = 0 + 11.33333333

Combine like terms: -11.33333333 + 11.33333333 = 0.00000000
0.00000000 + -2a + a2 = 0 + 11.33333333
-2a + a2 = 0 + 11.33333333

Combine like terms: 0 + 11.33333333 = 11.33333333
-2a + a2 = 11.33333333

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 = 11.33333333 + 1

Reorder the terms:
1 + -2a + a2 = 11.33333333 + 1

Combine like terms: 11.33333333 + 1 = 12.33333333
1 + -2a + a2 = 12.33333333

Factor a perfect square on the left side:
(a + -1)(a + -1) = 12.33333333

Calculate the square root of the right side: 3.511884584

Break this problem into two subproblems by setting 
(a + -1) equal to 3.511884584 and -3.511884584.

Subproblem 1

a + -1 = 3.511884584 Simplifying a + -1 = 3.511884584 Reorder the terms: -1 + a = 3.511884584 Solving -1 + a = 3.511884584 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 = 3.511884584 + 1 Combine like terms: -1 + 1 = 0 0 + a = 3.511884584 + 1 a = 3.511884584 + 1 Combine like terms: 3.511884584 + 1 = 4.511884584 a = 4.511884584 Simplifying a = 4.511884584

Subproblem 2

a + -1 = -3.511884584 Simplifying a + -1 = -3.511884584 Reorder the terms: -1 + a = -3.511884584 Solving -1 + a = -3.511884584 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 = -3.511884584 + 1 Combine like terms: -1 + 1 = 0 0 + a = -3.511884584 + 1 a = -3.511884584 + 1 Combine like terms: -3.511884584 + 1 = -2.511884584 a = -2.511884584 Simplifying a = -2.511884584

Solution

The solution to the problem is based on the solutions from the subproblems. a = {4.511884584, -2.511884584}

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