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Simplifying 6a2 + -12a = 12 Reorder the terms: -12a + 6a2 = 12 Solving -12a + 6a2 = 12 Solving for variable 'a'. Reorder the terms: -12 + -12a + 6a2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + -12a + 6a2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-2 + -2a + a2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-2 + -2a + a2)' equal to zero and attempt to solve: Simplifying -2 + -2a + a2 = 0 Solving -2 + -2a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -2a + 2 + a2 = 0 + 2 Reorder the terms: -2 + 2 + -2a + a2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -2a + a2 = 0 + 2 -2a + a2 = 0 + 2 Combine like terms: 0 + 2 = 2 -2a + a2 = 2 The a term is -2a. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2a + 1 + a2 = 2 + 1 Reorder the terms: 1 + -2a + a2 = 2 + 1 Combine like terms: 2 + 1 = 3 1 + -2a + a2 = 3 Factor a perfect square on the left side: (a + -1)(a + -1) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (a + -1) equal to 1.732050808 and -1.732050808.Subproblem 1
a + -1 = 1.732050808 Simplifying a + -1 = 1.732050808 Reorder the terms: -1 + a = 1.732050808 Solving -1 + a = 1.732050808 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + a = 1.732050808 + 1 Combine like terms: -1 + 1 = 0 0 + a = 1.732050808 + 1 a = 1.732050808 + 1 Combine like terms: 1.732050808 + 1 = 2.732050808 a = 2.732050808 Simplifying a = 2.732050808Subproblem 2
a + -1 = -1.732050808 Simplifying a + -1 = -1.732050808 Reorder the terms: -1 + a = -1.732050808 Solving -1 + a = -1.732050808 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + a = -1.732050808 + 1 Combine like terms: -1 + 1 = 0 0 + a = -1.732050808 + 1 a = -1.732050808 + 1 Combine like terms: -1.732050808 + 1 = -0.732050808 a = -0.732050808 Simplifying a = -0.732050808Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.732050808, -0.732050808}Solution
a = {2.732050808, -0.732050808}
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