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Simplifying -25a6 + 10a5 + 45a4 = 0 Reorder the terms: 45a4 + 10a5 + -25a6 = 0 Solving 45a4 + 10a5 + -25a6 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '5a4'. 5a4(9 + 2a + -5a2) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'a4' equal to zero and attempt to solve: Simplifying a4 = 0 Solving a4 = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a4 = 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 = 1.556465997 a = 1.556465997 Simplifying a = 1.556465997Subproblem 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 = -1.156465997 a = -1.156465997 Simplifying a = -1.156465997Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.556465997, -1.156465997}Solution
a = {1.556465997, -1.156465997}
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