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Simplifying 4a(a2 + 7a + 4) = 0 Reorder the terms: 4a(4 + 7a + a2) = 0 (4 * 4a + 7a * 4a + a2 * 4a) = 0 (16a + 28a2 + 4a3) = 0 Solving 16a + 28a2 + 4a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4a'. 4a(4 + 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 '(4 + 7a + a2)' equal to zero and attempt to solve: Simplifying 4 + 7a + a2 = 0 Solving 4 + 7a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 7a + -4 + a2 = 0 + -4 Reorder the terms: 4 + -4 + 7a + a2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 7a + a2 = 0 + -4 7a + a2 = 0 + -4 Combine like terms: 0 + -4 = -4 7a + a2 = -4 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 = -4 + 12.25 Reorder the terms: 12.25 + 7a + a2 = -4 + 12.25 Combine like terms: -4 + 12.25 = 8.25 12.25 + 7a + a2 = 8.25 Factor a perfect square on the left side: (a + 3.5)(a + 3.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (a + 3.5) equal to 2.872281323 and -2.872281323.Subproblem 1
a + 3.5 = 2.872281323 Simplifying a + 3.5 = 2.872281323 Reorder the terms: 3.5 + a = 2.872281323 Solving 3.5 + a = 2.872281323 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 = 2.872281323 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + a = 2.872281323 + -3.5 a = 2.872281323 + -3.5 Combine like terms: 2.872281323 + -3.5 = -0.627718677 a = -0.627718677 Simplifying a = -0.627718677Subproblem 2
a + 3.5 = -2.872281323 Simplifying a + 3.5 = -2.872281323 Reorder the terms: 3.5 + a = -2.872281323 Solving 3.5 + a = -2.872281323 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 = -2.872281323 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + a = -2.872281323 + -3.5 a = -2.872281323 + -3.5 Combine like terms: -2.872281323 + -3.5 = -6.372281323 a = -6.372281323 Simplifying a = -6.372281323Solution
The solution to the problem is based on the solutions from the subproblems. a = {-0.627718677, -6.372281323}Solution
a = {0, -0.627718677, -6.372281323}
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