2a^2-6=3a

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


Simplifying
2a2 + -6 = 3a

Reorder the terms:
-6 + 2a2 = 3a

Solving
-6 + 2a2 = 3a

Solving for variable 'a'.

Reorder the terms:
-6 + -3a + 2a2 = 3a + -3a

Combine like terms: 3a + -3a = 0
-6 + -3a + 2a2 = 0

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

Divide each side by '2'.
-3 + -1.5a + a2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -1.5a + 3 + a2 = 0 + 3

Reorder the terms:
-3 + 3 + -1.5a + a2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1.5a + a2 = 0 + 3
-1.5a + a2 = 0 + 3

Combine like terms: 0 + 3 = 3
-1.5a + a2 = 3

The a term is -1.5a.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5a + 0.5625 + a2 = 3 + 0.5625

Reorder the terms:
0.5625 + -1.5a + a2 = 3 + 0.5625

Combine like terms: 3 + 0.5625 = 3.5625
0.5625 + -1.5a + a2 = 3.5625

Factor a perfect square on the left side:
(a + -0.75)(a + -0.75) = 3.5625

Calculate the square root of the right side: 1.887458609

Break this problem into two subproblems by setting 
(a + -0.75) equal to 1.887458609 and -1.887458609.

Subproblem 1

a + -0.75 = 1.887458609 Simplifying a + -0.75 = 1.887458609 Reorder the terms: -0.75 + a = 1.887458609 Solving -0.75 + a = 1.887458609 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + a = 1.887458609 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + a = 1.887458609 + 0.75 a = 1.887458609 + 0.75 Combine like terms: 1.887458609 + 0.75 = 2.637458609 a = 2.637458609 Simplifying a = 2.637458609

Subproblem 2

a + -0.75 = -1.887458609 Simplifying a + -0.75 = -1.887458609 Reorder the terms: -0.75 + a = -1.887458609 Solving -0.75 + a = -1.887458609 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + a = -1.887458609 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + a = -1.887458609 + 0.75 a = -1.887458609 + 0.75 Combine like terms: -1.887458609 + 0.75 = -1.137458609 a = -1.137458609 Simplifying a = -1.137458609

Solution

The solution to the problem is based on the solutions from the subproblems. a = {2.637458609, -1.137458609}

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