4a^2-12a+3=0

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Solution for 4a^2-12a+3=0 equation:


Simplifying
4a2 + -12a + 3 = 0

Reorder the terms:
3 + -12a + 4a2 = 0

Solving
3 + -12a + 4a2 = 0

Solving for variable 'a'.

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

Divide each side by '4'.
0.75 + -3a + a2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + -3a + -0.75 + a2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + -3a + a2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + -3a + a2 = 0 + -0.75
-3a + a2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
-3a + a2 = -0.75

The a term is -3a.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3a + 2.25 + a2 = -0.75 + 2.25

Reorder the terms:
2.25 + -3a + a2 = -0.75 + 2.25

Combine like terms: -0.75 + 2.25 = 1.5
2.25 + -3a + a2 = 1.5

Factor a perfect square on the left side:
(a + -1.5)(a + -1.5) = 1.5

Calculate the square root of the right side: 1.224744871

Break this problem into two subproblems by setting 
(a + -1.5) equal to 1.224744871 and -1.224744871.

Subproblem 1

a + -1.5 = 1.224744871 Simplifying a + -1.5 = 1.224744871 Reorder the terms: -1.5 + a = 1.224744871 Solving -1.5 + a = 1.224744871 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + a = 1.224744871 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + a = 1.224744871 + 1.5 a = 1.224744871 + 1.5 Combine like terms: 1.224744871 + 1.5 = 2.724744871 a = 2.724744871 Simplifying a = 2.724744871

Subproblem 2

a + -1.5 = -1.224744871 Simplifying a + -1.5 = -1.224744871 Reorder the terms: -1.5 + a = -1.224744871 Solving -1.5 + a = -1.224744871 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + a = -1.224744871 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + a = -1.224744871 + 1.5 a = -1.224744871 + 1.5 Combine like terms: -1.224744871 + 1.5 = 0.275255129 a = 0.275255129 Simplifying a = 0.275255129

Solution

The solution to the problem is based on the solutions from the subproblems. a = {2.724744871, 0.275255129}

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