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Simplifying 3a(a + 18) = 18 Reorder the terms: 3a(18 + a) = 18 (18 * 3a + a * 3a) = 18 (54a + 3a2) = 18 Solving 54a + 3a2 = 18 Solving for variable 'a'. Reorder the terms: -18 + 54a + 3a2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + 54a + 3a2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-6 + 18a + a2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-6 + 18a + a2)' equal to zero and attempt to solve: Simplifying -6 + 18a + a2 = 0 Solving -6 + 18a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 18a + 6 + a2 = 0 + 6 Reorder the terms: -6 + 6 + 18a + a2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 18a + a2 = 0 + 6 18a + a2 = 0 + 6 Combine like terms: 0 + 6 = 6 18a + a2 = 6 The a term is 18a. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18a + 81 + a2 = 6 + 81 Reorder the terms: 81 + 18a + a2 = 6 + 81 Combine like terms: 6 + 81 = 87 81 + 18a + a2 = 87 Factor a perfect square on the left side: (a + 9)(a + 9) = 87 Calculate the square root of the right side: 9.327379053 Break this problem into two subproblems by setting (a + 9) equal to 9.327379053 and -9.327379053.Subproblem 1
a + 9 = 9.327379053 Simplifying a + 9 = 9.327379053 Reorder the terms: 9 + a = 9.327379053 Solving 9 + a = 9.327379053 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + a = 9.327379053 + -9 Combine like terms: 9 + -9 = 0 0 + a = 9.327379053 + -9 a = 9.327379053 + -9 Combine like terms: 9.327379053 + -9 = 0.327379053 a = 0.327379053 Simplifying a = 0.327379053Subproblem 2
a + 9 = -9.327379053 Simplifying a + 9 = -9.327379053 Reorder the terms: 9 + a = -9.327379053 Solving 9 + a = -9.327379053 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + a = -9.327379053 + -9 Combine like terms: 9 + -9 = 0 0 + a = -9.327379053 + -9 a = -9.327379053 + -9 Combine like terms: -9.327379053 + -9 = -18.327379053 a = -18.327379053 Simplifying a = -18.327379053Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.327379053, -18.327379053}Solution
a = {0.327379053, -18.327379053}
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