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Simplifying -5a2 + -30a + -44 = 0 Reorder the terms: -44 + -30a + -5a2 = 0 Solving -44 + -30a + -5a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '-1'. -1(44 + 30a + 5a2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(44 + 30a + 5a2)' equal to zero and attempt to solve: Simplifying 44 + 30a + 5a2 = 0 Solving 44 + 30a + 5a2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 8.8 + 6a + a2 = 0 Move the constant term to the right: Add '-8.8' to each side of the equation. 8.8 + 6a + -8.8 + a2 = 0 + -8.8 Reorder the terms: 8.8 + -8.8 + 6a + a2 = 0 + -8.8 Combine like terms: 8.8 + -8.8 = 0.0 0.0 + 6a + a2 = 0 + -8.8 6a + a2 = 0 + -8.8 Combine like terms: 0 + -8.8 = -8.8 6a + a2 = -8.8 The a term is 6a. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6a + 9 + a2 = -8.8 + 9 Reorder the terms: 9 + 6a + a2 = -8.8 + 9 Combine like terms: -8.8 + 9 = 0.2 9 + 6a + a2 = 0.2 Factor a perfect square on the left side: (a + 3)(a + 3) = 0.2 Calculate the square root of the right side: 0.447213596 Break this problem into two subproblems by setting (a + 3) equal to 0.447213596 and -0.447213596.Subproblem 1
a + 3 = 0.447213596 Simplifying a + 3 = 0.447213596 Reorder the terms: 3 + a = 0.447213596 Solving 3 + a = 0.447213596 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + a = 0.447213596 + -3 Combine like terms: 3 + -3 = 0 0 + a = 0.447213596 + -3 a = 0.447213596 + -3 Combine like terms: 0.447213596 + -3 = -2.552786404 a = -2.552786404 Simplifying a = -2.552786404Subproblem 2
a + 3 = -0.447213596 Simplifying a + 3 = -0.447213596 Reorder the terms: 3 + a = -0.447213596 Solving 3 + a = -0.447213596 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + a = -0.447213596 + -3 Combine like terms: 3 + -3 = 0 0 + a = -0.447213596 + -3 a = -0.447213596 + -3 Combine like terms: -0.447213596 + -3 = -3.447213596 a = -3.447213596 Simplifying a = -3.447213596Solution
The solution to the problem is based on the solutions from the subproblems. a = {-2.552786404, -3.447213596}Solution
a = {-2.552786404, -3.447213596}
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