3a^2-12a=10

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Solution for 3a^2-12a=10 equation:


Simplifying
3a2 + -12a = 10

Reorder the terms:
-12a + 3a2 = 10

Solving
-12a + 3a2 = 10

Solving for variable 'a'.

Reorder the terms:
-10 + -12a + 3a2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -12a + 3a2 = 0

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

Divide each side by '3'.
-3.333333333 + -4a + a2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + -4a + 3.333333333 + a2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + -4a + a2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + -4a + a2 = 0 + 3.333333333
-4a + a2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
-4a + a2 = 3.333333333

The a term is -4a.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4a + 4 + a2 = 3.333333333 + 4

Reorder the terms:
4 + -4a + a2 = 3.333333333 + 4

Combine like terms: 3.333333333 + 4 = 7.333333333
4 + -4a + a2 = 7.333333333

Factor a perfect square on the left side:
(a + -2)(a + -2) = 7.333333333

Calculate the square root of the right side: 2.708012801

Break this problem into two subproblems by setting 
(a + -2) equal to 2.708012801 and -2.708012801.

Subproblem 1

a + -2 = 2.708012801 Simplifying a + -2 = 2.708012801 Reorder the terms: -2 + a = 2.708012801 Solving -2 + a = 2.708012801 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + a = 2.708012801 + 2 Combine like terms: -2 + 2 = 0 0 + a = 2.708012801 + 2 a = 2.708012801 + 2 Combine like terms: 2.708012801 + 2 = 4.708012801 a = 4.708012801 Simplifying a = 4.708012801

Subproblem 2

a + -2 = -2.708012801 Simplifying a + -2 = -2.708012801 Reorder the terms: -2 + a = -2.708012801 Solving -2 + a = -2.708012801 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + a = -2.708012801 + 2 Combine like terms: -2 + 2 = 0 0 + a = -2.708012801 + 2 a = -2.708012801 + 2 Combine like terms: -2.708012801 + 2 = -0.708012801 a = -0.708012801 Simplifying a = -0.708012801

Solution

The solution to the problem is based on the solutions from the subproblems. a = {4.708012801, -0.708012801}

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