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Simplifying -12a3b + -14a2b + 16ab = 0 Reorder the terms: 16ab + -14a2b + -12a3b = 0 Solving 16ab + -14a2b + -12a3b = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2ab'. 2ab(8 + -7a + -6a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'ab' equal to zero and attempt to solve: Simplifying ab = 0 Solving ab = 0 Move all terms containing a to the left, all other terms to the right. Simplifying ab = 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 '(8 + -7a + -6a2)' equal to zero and attempt to solve: Simplifying 8 + -7a + -6a2 = 0 Solving 8 + -7a + -6a2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -1.333333333 + 1.166666667a + a2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + 1.166666667a + 1.333333333 + a2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + 1.166666667a + a2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + 1.166666667a + a2 = 0 + 1.333333333 1.166666667a + a2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 1.166666667a + a2 = 1.333333333 The a term is 1.166666667a. Take half its coefficient (0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. 1.166666667a + 0.3402777780 + a2 = 1.333333333 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667a + a2 = 1.333333333 + 0.3402777780 Combine like terms: 1.333333333 + 0.3402777780 = 1.673611111 0.3402777780 + 1.166666667a + a2 = 1.673611111 Factor a perfect square on the left side: (a + 0.5833333335)(a + 0.5833333335) = 1.673611111 Calculate the square root of the right side: 1.293681225 Break this problem into two subproblems by setting (a + 0.5833333335) equal to 1.293681225 and -1.293681225.Subproblem 1
a + 0.5833333335 = 1.293681225 Simplifying a + 0.5833333335 = 1.293681225 Reorder the terms: 0.5833333335 + a = 1.293681225 Solving 0.5833333335 + a = 1.293681225 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + a = 1.293681225 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + a = 1.293681225 + -0.5833333335 a = 1.293681225 + -0.5833333335 Combine like terms: 1.293681225 + -0.5833333335 = 0.7103478915 a = 0.7103478915 Simplifying a = 0.7103478915Subproblem 2
a + 0.5833333335 = -1.293681225 Simplifying a + 0.5833333335 = -1.293681225 Reorder the terms: 0.5833333335 + a = -1.293681225 Solving 0.5833333335 + a = -1.293681225 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + a = -1.293681225 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + a = -1.293681225 + -0.5833333335 a = -1.293681225 + -0.5833333335 Combine like terms: -1.293681225 + -0.5833333335 = -1.8770145585 a = -1.8770145585 Simplifying a = -1.8770145585Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.7103478915, -1.8770145585}Solution
a = {0.7103478915, -1.8770145585}
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