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Simplifying 5a5 + 2a4 + -9a3 = 0 Reorder the terms: -9a3 + 2a4 + 5a5 = 0 Solving -9a3 + 2a4 + 5a5 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a3'. a3(-9 + 2a + 5a2) = 0Subproblem 1
Set the factor 'a3' equal to zero and attempt to solve: Simplifying a3 = 0 Solving a3 = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-9 + 2a + 5a2)' equal to zero and attempt to solve: Simplifying -9 + 2a + 5a2 = 0 Solving -9 + 2a + 5a2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.8 + 0.4a + a2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + 0.4a + 1.8 + a2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + 0.4a + a2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + 0.4a + a2 = 0 + 1.8 0.4a + a2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 0.4a + a2 = 1.8 The a term is 0.4a. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4a + 0.04 + a2 = 1.8 + 0.04 Reorder the terms: 0.04 + 0.4a + a2 = 1.8 + 0.04 Combine like terms: 1.8 + 0.04 = 1.84 0.04 + 0.4a + a2 = 1.84 Factor a perfect square on the left side: (a + 0.2)(a + 0.2) = 1.84 Calculate the square root of the right side: 1.356465997 Break this problem into two subproblems by setting (a + 0.2) equal to 1.356465997 and -1.356465997.Subproblem 1
a + 0.2 = 1.356465997 Simplifying a + 0.2 = 1.356465997 Reorder the terms: 0.2 + a = 1.356465997 Solving 0.2 + a = 1.356465997 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + a = 1.356465997 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + a = 1.356465997 + -0.2 a = 1.356465997 + -0.2 Combine like terms: 1.356465997 + -0.2 = 1.156465997 a = 1.156465997 Simplifying a = 1.156465997Subproblem 2
a + 0.2 = -1.356465997 Simplifying a + 0.2 = -1.356465997 Reorder the terms: 0.2 + a = -1.356465997 Solving 0.2 + a = -1.356465997 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + a = -1.356465997 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + a = -1.356465997 + -0.2 a = -1.356465997 + -0.2 Combine like terms: -1.356465997 + -0.2 = -1.556465997 a = -1.556465997 Simplifying a = -1.556465997Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.156465997, -1.556465997}Solution
a = {1.156465997, -1.556465997}
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