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Simplifying -4a3 + -28a2 + -8a = 0 Reorder the terms: -8a + -28a2 + -4a3 = 0 Solving -8a + -28a2 + -4a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '-4a'. -4a(2 + 7a + a2) = 0 Ignore the factor -4.Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(2 + 7a + a2)' equal to zero and attempt to solve: Simplifying 2 + 7a + a2 = 0 Solving 2 + 7a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 7a + -2 + a2 = 0 + -2 Reorder the terms: 2 + -2 + 7a + a2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 7a + a2 = 0 + -2 7a + a2 = 0 + -2 Combine like terms: 0 + -2 = -2 7a + a2 = -2 The a term is 7a. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7a + 12.25 + a2 = -2 + 12.25 Reorder the terms: 12.25 + 7a + a2 = -2 + 12.25 Combine like terms: -2 + 12.25 = 10.25 12.25 + 7a + a2 = 10.25 Factor a perfect square on the left side: (a + 3.5)(a + 3.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (a + 3.5) equal to 3.201562119 and -3.201562119.Subproblem 1
a + 3.5 = 3.201562119 Simplifying a + 3.5 = 3.201562119 Reorder the terms: 3.5 + a = 3.201562119 Solving 3.5 + a = 3.201562119 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + a = 3.201562119 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + a = 3.201562119 + -3.5 a = 3.201562119 + -3.5 Combine like terms: 3.201562119 + -3.5 = -0.298437881 a = -0.298437881 Simplifying a = -0.298437881Subproblem 2
a + 3.5 = -3.201562119 Simplifying a + 3.5 = -3.201562119 Reorder the terms: 3.5 + a = -3.201562119 Solving 3.5 + a = -3.201562119 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + a = -3.201562119 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + a = -3.201562119 + -3.5 a = -3.201562119 + -3.5 Combine like terms: -3.201562119 + -3.5 = -6.701562119 a = -6.701562119 Simplifying a = -6.701562119Solution
The solution to the problem is based on the solutions from the subproblems. a = {-0.298437881, -6.701562119}Solution
a = {0, -0.298437881, -6.701562119}
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