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Simplifying 3a2 + 15a + -3 = 0 Reorder the terms: -3 + 15a + 3a2 = 0 Solving -3 + 15a + 3a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + 5a + a2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + 5a + a2)' equal to zero and attempt to solve: Simplifying -1 + 5a + a2 = 0 Solving -1 + 5a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 5a + 1 + a2 = 0 + 1 Reorder the terms: -1 + 1 + 5a + a2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 5a + a2 = 0 + 1 5a + a2 = 0 + 1 Combine like terms: 0 + 1 = 1 5a + a2 = 1 The a term is 5a. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5a + 6.25 + a2 = 1 + 6.25 Reorder the terms: 6.25 + 5a + a2 = 1 + 6.25 Combine like terms: 1 + 6.25 = 7.25 6.25 + 5a + a2 = 7.25 Factor a perfect square on the left side: (a + 2.5)(a + 2.5) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (a + 2.5) equal to 2.692582404 and -2.692582404.Subproblem 1
a + 2.5 = 2.692582404 Simplifying a + 2.5 = 2.692582404 Reorder the terms: 2.5 + a = 2.692582404 Solving 2.5 + a = 2.692582404 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + a = 2.692582404 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + a = 2.692582404 + -2.5 a = 2.692582404 + -2.5 Combine like terms: 2.692582404 + -2.5 = 0.192582404 a = 0.192582404 Simplifying a = 0.192582404Subproblem 2
a + 2.5 = -2.692582404 Simplifying a + 2.5 = -2.692582404 Reorder the terms: 2.5 + a = -2.692582404 Solving 2.5 + a = -2.692582404 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + a = -2.692582404 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + a = -2.692582404 + -2.5 a = -2.692582404 + -2.5 Combine like terms: -2.692582404 + -2.5 = -5.192582404 a = -5.192582404 Simplifying a = -5.192582404Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.192582404, -5.192582404}Solution
a = {0.192582404, -5.192582404}
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