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Simplifying 16a = a2(2a + -12) Reorder the terms: 16a = a2(-12 + 2a) 16a = (-12 * a2 + 2a * a2) 16a = (-12a2 + 2a3) Solving 16a = -12a2 + 2a3 Solving for variable 'a'. Reorder the terms: 16a + 12a2 + -2a3 = -12a2 + 12a2 + 2a3 + -2a3 Combine like terms: -12a2 + 12a2 = 0 16a + 12a2 + -2a3 = 0 + 2a3 + -2a3 16a + 12a2 + -2a3 = 2a3 + -2a3 Combine like terms: 2a3 + -2a3 = 0 16a + 12a2 + -2a3 = 0 Factor out the Greatest Common Factor (GCF), '2a'. 2a(8 + 6a + -1a2) = 0 Ignore the factor 2.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 '(8 + 6a + -1a2)' equal to zero and attempt to solve: Simplifying 8 + 6a + -1a2 = 0 Solving 8 + 6a + -1a2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -8 + -6a + a2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -6a + 8 + a2 = 0 + 8 Reorder the terms: -8 + 8 + -6a + a2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -6a + a2 = 0 + 8 -6a + a2 = 0 + 8 Combine like terms: 0 + 8 = 8 -6a + a2 = 8 The a term is -6a. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6a + 9 + a2 = 8 + 9 Reorder the terms: 9 + -6a + a2 = 8 + 9 Combine like terms: 8 + 9 = 17 9 + -6a + a2 = 17 Factor a perfect square on the left side: (a + -3)(a + -3) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (a + -3) equal to 4.123105626 and -4.123105626.Subproblem 1
a + -3 = 4.123105626 Simplifying a + -3 = 4.123105626 Reorder the terms: -3 + a = 4.123105626 Solving -3 + a = 4.123105626 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + a = 4.123105626 + 3 Combine like terms: -3 + 3 = 0 0 + a = 4.123105626 + 3 a = 4.123105626 + 3 Combine like terms: 4.123105626 + 3 = 7.123105626 a = 7.123105626 Simplifying a = 7.123105626Subproblem 2
a + -3 = -4.123105626 Simplifying a + -3 = -4.123105626 Reorder the terms: -3 + a = -4.123105626 Solving -3 + a = -4.123105626 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + a = -4.123105626 + 3 Combine like terms: -3 + 3 = 0 0 + a = -4.123105626 + 3 a = -4.123105626 + 3 Combine like terms: -4.123105626 + 3 = -1.123105626 a = -1.123105626 Simplifying a = -1.123105626Solution
The solution to the problem is based on the solutions from the subproblems. a = {7.123105626, -1.123105626}Solution
a = {0, 7.123105626, -1.123105626}
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