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Simplifying 6a2 + -12a + -38 = -5 Reorder the terms: -38 + -12a + 6a2 = -5 Solving -38 + -12a + 6a2 = -5 Solving for variable 'a'. Reorder the terms: -38 + 5 + -12a + 6a2 = -5 + 5 Combine like terms: -38 + 5 = -33 -33 + -12a + 6a2 = -5 + 5 Combine like terms: -5 + 5 = 0 -33 + -12a + 6a2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-11 + -4a + 2a2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-11 + -4a + 2a2)' equal to zero and attempt to solve: Simplifying -11 + -4a + 2a2 = 0 Solving -11 + -4a + 2a2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5.5 + -2a + a2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + -2a + 5.5 + a2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + -2a + a2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + -2a + a2 = 0 + 5.5 -2a + a2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 -2a + a2 = 5.5 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 = 5.5 + 1 Reorder the terms: 1 + -2a + a2 = 5.5 + 1 Combine like terms: 5.5 + 1 = 6.5 1 + -2a + a2 = 6.5 Factor a perfect square on the left side: (a + -1)(a + -1) = 6.5 Calculate the square root of the right side: 2.549509757 Break this problem into two subproblems by setting (a + -1) equal to 2.549509757 and -2.549509757.Subproblem 1
a + -1 = 2.549509757 Simplifying a + -1 = 2.549509757 Reorder the terms: -1 + a = 2.549509757 Solving -1 + a = 2.549509757 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 = 2.549509757 + 1 Combine like terms: -1 + 1 = 0 0 + a = 2.549509757 + 1 a = 2.549509757 + 1 Combine like terms: 2.549509757 + 1 = 3.549509757 a = 3.549509757 Simplifying a = 3.549509757Subproblem 2
a + -1 = -2.549509757 Simplifying a + -1 = -2.549509757 Reorder the terms: -1 + a = -2.549509757 Solving -1 + a = -2.549509757 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 = -2.549509757 + 1 Combine like terms: -1 + 1 = 0 0 + a = -2.549509757 + 1 a = -2.549509757 + 1 Combine like terms: -2.549509757 + 1 = -1.549509757 a = -1.549509757 Simplifying a = -1.549509757Solution
The solution to the problem is based on the solutions from the subproblems. a = {3.549509757, -1.549509757}Solution
a = {3.549509757, -1.549509757}
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