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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 = 14.25 12.25 + -7a + a2 = 14.25 Factor a perfect square on the left side: (a + -3.5)(a + -3.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (a + -3.5) equal to 3.774917218 and -3.774917218.Subproblem 1
a + -3.5 = 3.774917218 Simplifying a + -3.5 = 3.774917218 Reorder the terms: -3.5 + a = 3.774917218 Solving -3.5 + a = 3.774917218 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 = 3.774917218 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + a = 3.774917218 + 3.5 a = 3.774917218 + 3.5 Combine like terms: 3.774917218 + 3.5 = 7.274917218 a = 7.274917218 Simplifying a = 7.274917218Subproblem 2
a + -3.5 = -3.774917218 Simplifying a + -3.5 = -3.774917218 Reorder the terms: -3.5 + a = -3.774917218 Solving -3.5 + a = -3.774917218 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 = -3.774917218 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + a = -3.774917218 + 3.5 a = -3.774917218 + 3.5 Combine like terms: -3.774917218 + 3.5 = -0.274917218 a = -0.274917218 Simplifying a = -0.274917218Solution
The solution to the problem is based on the solutions from the subproblems. a = {7.274917218, -0.274917218}Solution
a = {0, 7.274917218, -0.274917218}
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