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Simplifying -3a2 + -54a + -81 = 0 Reorder the terms: -81 + -54a + -3a2 = 0 Solving -81 + -54a + -3a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '-3'. -3(27 + 18a + a2) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(27 + 18a + a2)' equal to zero and attempt to solve: Simplifying 27 + 18a + a2 = 0 Solving 27 + 18a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-27' to each side of the equation. 27 + 18a + -27 + a2 = 0 + -27 Reorder the terms: 27 + -27 + 18a + a2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + 18a + a2 = 0 + -27 18a + a2 = 0 + -27 Combine like terms: 0 + -27 = -27 18a + a2 = -27 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 = -27 + 81 Reorder the terms: 81 + 18a + a2 = -27 + 81 Combine like terms: -27 + 81 = 54 81 + 18a + a2 = 54 Factor a perfect square on the left side: (a + 9)(a + 9) = 54 Calculate the square root of the right side: 7.348469228 Break this problem into two subproblems by setting (a + 9) equal to 7.348469228 and -7.348469228.Subproblem 1
a + 9 = 7.348469228 Simplifying a + 9 = 7.348469228 Reorder the terms: 9 + a = 7.348469228 Solving 9 + a = 7.348469228 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 = 7.348469228 + -9 Combine like terms: 9 + -9 = 0 0 + a = 7.348469228 + -9 a = 7.348469228 + -9 Combine like terms: 7.348469228 + -9 = -1.651530772 a = -1.651530772 Simplifying a = -1.651530772Subproblem 2
a + 9 = -7.348469228 Simplifying a + 9 = -7.348469228 Reorder the terms: 9 + a = -7.348469228 Solving 9 + a = -7.348469228 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 = -7.348469228 + -9 Combine like terms: 9 + -9 = 0 0 + a = -7.348469228 + -9 a = -7.348469228 + -9 Combine like terms: -7.348469228 + -9 = -16.348469228 a = -16.348469228 Simplifying a = -16.348469228Solution
The solution to the problem is based on the solutions from the subproblems. a = {-1.651530772, -16.348469228}Solution
a = {-1.651530772, -16.348469228}
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