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Simplifying 4(a2 + 18a + 81) = 120 Reorder the terms: 4(81 + 18a + a2) = 120 (81 * 4 + 18a * 4 + a2 * 4) = 120 (324 + 72a + 4a2) = 120 Solving 324 + 72a + 4a2 = 120 Solving for variable 'a'. Reorder the terms: 324 + -120 + 72a + 4a2 = 120 + -120 Combine like terms: 324 + -120 = 204 204 + 72a + 4a2 = 120 + -120 Combine like terms: 120 + -120 = 0 204 + 72a + 4a2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(51 + 18a + a2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(51 + 18a + a2)' equal to zero and attempt to solve: Simplifying 51 + 18a + a2 = 0 Solving 51 + 18a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-51' to each side of the equation. 51 + 18a + -51 + a2 = 0 + -51 Reorder the terms: 51 + -51 + 18a + a2 = 0 + -51 Combine like terms: 51 + -51 = 0 0 + 18a + a2 = 0 + -51 18a + a2 = 0 + -51 Combine like terms: 0 + -51 = -51 18a + a2 = -51 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 = -51 + 81 Reorder the terms: 81 + 18a + a2 = -51 + 81 Combine like terms: -51 + 81 = 30 81 + 18a + a2 = 30 Factor a perfect square on the left side: (a + 9)(a + 9) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (a + 9) equal to 5.477225575 and -5.477225575.Subproblem 1
a + 9 = 5.477225575 Simplifying a + 9 = 5.477225575 Reorder the terms: 9 + a = 5.477225575 Solving 9 + a = 5.477225575 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 = 5.477225575 + -9 Combine like terms: 9 + -9 = 0 0 + a = 5.477225575 + -9 a = 5.477225575 + -9 Combine like terms: 5.477225575 + -9 = -3.522774425 a = -3.522774425 Simplifying a = -3.522774425Subproblem 2
a + 9 = -5.477225575 Simplifying a + 9 = -5.477225575 Reorder the terms: 9 + a = -5.477225575 Solving 9 + a = -5.477225575 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 = -5.477225575 + -9 Combine like terms: 9 + -9 = 0 0 + a = -5.477225575 + -9 a = -5.477225575 + -9 Combine like terms: -5.477225575 + -9 = -14.477225575 a = -14.477225575 Simplifying a = -14.477225575Solution
The solution to the problem is based on the solutions from the subproblems. a = {-3.522774425, -14.477225575}Solution
a = {-3.522774425, -14.477225575}
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