4a^2-4a-12=0

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


Simplifying
4a2 + -4a + -12 = 0

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

Solving
-12 + -4a + 4a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-3 + -1a + a2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-3 + -1a + a2)' equal to zero and attempt to solve: Simplifying -3 + -1a + a2 = 0 Solving -3 + -1a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -1a + 3 + a2 = 0 + 3 Reorder the terms: -3 + 3 + -1a + a2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1a + a2 = 0 + 3 -1a + a2 = 0 + 3 Combine like terms: 0 + 3 = 3 -1a + a2 = 3 The a term is -1a. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1a + 0.25 + a2 = 3 + 0.25 Reorder the terms: 0.25 + -1a + a2 = 3 + 0.25 Combine like terms: 3 + 0.25 = 3.25 0.25 + -1a + a2 = 3.25 Factor a perfect square on the left side: (a + -0.5)(a + -0.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (a + -0.5) equal to 1.802775638 and -1.802775638.

Subproblem 1

a + -0.5 = 1.802775638 Simplifying a + -0.5 = 1.802775638 Reorder the terms: -0.5 + a = 1.802775638 Solving -0.5 + a = 1.802775638 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + a = 1.802775638 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + a = 1.802775638 + 0.5 a = 1.802775638 + 0.5 Combine like terms: 1.802775638 + 0.5 = 2.302775638 a = 2.302775638 Simplifying a = 2.302775638

Subproblem 2

a + -0.5 = -1.802775638 Simplifying a + -0.5 = -1.802775638 Reorder the terms: -0.5 + a = -1.802775638 Solving -0.5 + a = -1.802775638 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + a = -1.802775638 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + a = -1.802775638 + 0.5 a = -1.802775638 + 0.5 Combine like terms: -1.802775638 + 0.5 = -1.302775638 a = -1.302775638 Simplifying a = -1.302775638

Solution

The solution to the problem is based on the solutions from the subproblems. a = {2.302775638, -1.302775638}

Solution

a = {2.302775638, -1.302775638}

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