3a^2-12a+3=a^2-4

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Solution for 3a^2-12a+3=a^2-4 equation:


Simplifying
3a2 + -12a + 3 = a2 + -4

Reorder the terms:
3 + -12a + 3a2 = a2 + -4

Reorder the terms:
3 + -12a + 3a2 = -4 + a2

Solving
3 + -12a + 3a2 = -4 + a2

Solving for variable 'a'.

Reorder the terms:
3 + 4 + -12a + 3a2 + -1a2 = -4 + a2 + 4 + -1a2

Combine like terms: 3 + 4 = 7
7 + -12a + 3a2 + -1a2 = -4 + a2 + 4 + -1a2

Combine like terms: 3a2 + -1a2 = 2a2
7 + -12a + 2a2 = -4 + a2 + 4 + -1a2

Reorder the terms:
7 + -12a + 2a2 = -4 + 4 + a2 + -1a2

Combine like terms: -4 + 4 = 0
7 + -12a + 2a2 = 0 + a2 + -1a2
7 + -12a + 2a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
7 + -12a + 2a2 = 0

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

Divide each side by '2'.
3.5 + -6a + a2 = 0

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + -6a + -3.5 + a2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + -6a + a2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + -6a + a2 = 0 + -3.5
-6a + a2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
-6a + a2 = -3.5

The a term is -6a.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6a + 9 + a2 = -3.5 + 9

Reorder the terms:
9 + -6a + a2 = -3.5 + 9

Combine like terms: -3.5 + 9 = 5.5
9 + -6a + a2 = 5.5

Factor a perfect square on the left side:
(a + -3)(a + -3) = 5.5

Calculate the square root of the right side: 2.34520788

Break this problem into two subproblems by setting 
(a + -3) equal to 2.34520788 and -2.34520788.

Subproblem 1

a + -3 = 2.34520788 Simplifying a + -3 = 2.34520788 Reorder the terms: -3 + a = 2.34520788 Solving -3 + a = 2.34520788 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + a = 2.34520788 + 3 Combine like terms: -3 + 3 = 0 0 + a = 2.34520788 + 3 a = 2.34520788 + 3 Combine like terms: 2.34520788 + 3 = 5.34520788 a = 5.34520788 Simplifying a = 5.34520788

Subproblem 2

a + -3 = -2.34520788 Simplifying a + -3 = -2.34520788 Reorder the terms: -3 + a = -2.34520788 Solving -3 + a = -2.34520788 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + a = -2.34520788 + 3 Combine like terms: -3 + 3 = 0 0 + a = -2.34520788 + 3 a = -2.34520788 + 3 Combine like terms: -2.34520788 + 3 = 0.65479212 a = 0.65479212 Simplifying a = 0.65479212

Solution

The solution to the problem is based on the solutions from the subproblems. a = {5.34520788, 0.65479212}

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