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Simplifying 3a2 + 18a + 9 = 0 Reorder the terms: 9 + 18a + 3a2 = 0 Solving 9 + 18a + 3a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3'. 3(3 + 6a + a2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + 6a + a2)' equal to zero and attempt to solve: Simplifying 3 + 6a + a2 = 0 Solving 3 + 6a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 6a + -3 + a2 = 0 + -3 Reorder the terms: 3 + -3 + 6a + a2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 6a + a2 = 0 + -3 6a + a2 = 0 + -3 Combine like terms: 0 + -3 = -3 6a + a2 = -3 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 = -3 + 9 Reorder the terms: 9 + 6a + a2 = -3 + 9 Combine like terms: -3 + 9 = 6 9 + 6a + a2 = 6 Factor a perfect square on the left side: (a + 3)(a + 3) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (a + 3) equal to 2.449489743 and -2.449489743.Subproblem 1
a + 3 = 2.449489743 Simplifying a + 3 = 2.449489743 Reorder the terms: 3 + a = 2.449489743 Solving 3 + a = 2.449489743 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 = 2.449489743 + -3 Combine like terms: 3 + -3 = 0 0 + a = 2.449489743 + -3 a = 2.449489743 + -3 Combine like terms: 2.449489743 + -3 = -0.550510257 a = -0.550510257 Simplifying a = -0.550510257Subproblem 2
a + 3 = -2.449489743 Simplifying a + 3 = -2.449489743 Reorder the terms: 3 + a = -2.449489743 Solving 3 + a = -2.449489743 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 = -2.449489743 + -3 Combine like terms: 3 + -3 = 0 0 + a = -2.449489743 + -3 a = -2.449489743 + -3 Combine like terms: -2.449489743 + -3 = -5.449489743 a = -5.449489743 Simplifying a = -5.449489743Solution
The solution to the problem is based on the solutions from the subproblems. a = {-0.550510257, -5.449489743}Solution
a = {-0.550510257, -5.449489743}
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