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Simplifying 5a2 + 9a + 2 = 0 Reorder the terms: 2 + 9a + 5a2 = 0 Solving 2 + 9a + 5a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + 1.8a + a2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + 1.8a + -0.4 + a2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + 1.8a + a2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + 1.8a + a2 = 0 + -0.4 1.8a + a2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 1.8a + a2 = -0.4 The a term is 1.8a. Take half its coefficient (0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. 1.8a + 0.81 + a2 = -0.4 + 0.81 Reorder the terms: 0.81 + 1.8a + a2 = -0.4 + 0.81 Combine like terms: -0.4 + 0.81 = 0.41 0.81 + 1.8a + a2 = 0.41 Factor a perfect square on the left side: (a + 0.9)(a + 0.9) = 0.41 Calculate the square root of the right side: 0.640312424 Break this problem into two subproblems by setting (a + 0.9) equal to 0.640312424 and -0.640312424.Subproblem 1
a + 0.9 = 0.640312424 Simplifying a + 0.9 = 0.640312424 Reorder the terms: 0.9 + a = 0.640312424 Solving 0.9 + a = 0.640312424 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + a = 0.640312424 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + a = 0.640312424 + -0.9 a = 0.640312424 + -0.9 Combine like terms: 0.640312424 + -0.9 = -0.259687576 a = -0.259687576 Simplifying a = -0.259687576Subproblem 2
a + 0.9 = -0.640312424 Simplifying a + 0.9 = -0.640312424 Reorder the terms: 0.9 + a = -0.640312424 Solving 0.9 + a = -0.640312424 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + a = -0.640312424 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + a = -0.640312424 + -0.9 a = -0.640312424 + -0.9 Combine like terms: -0.640312424 + -0.9 = -1.540312424 a = -1.540312424 Simplifying a = -1.540312424Solution
The solution to the problem is based on the solutions from the subproblems. a = {-0.259687576, -1.540312424}
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