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Simplifying -9a2 + 16a + 24 = 0 Reorder the terms: 24 + 16a + -9a2 = 0 Solving 24 + 16a + -9a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -2.666666667 + -1.777777778a + a2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + -1.777777778a + 2.666666667 + a2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + -1.777777778a + a2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + -1.777777778a + a2 = 0 + 2.666666667 -1.777777778a + a2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 -1.777777778a + a2 = 2.666666667 The a term is -1.777777778a. Take half its coefficient (-0.888888889). Square it (0.7901234570) and add it to both sides. Add '0.7901234570' to each side of the equation. -1.777777778a + 0.7901234570 + a2 = 2.666666667 + 0.7901234570 Reorder the terms: 0.7901234570 + -1.777777778a + a2 = 2.666666667 + 0.7901234570 Combine like terms: 2.666666667 + 0.7901234570 = 3.456790124 0.7901234570 + -1.777777778a + a2 = 3.456790124 Factor a perfect square on the left side: (a + -0.888888889)(a + -0.888888889) = 3.456790124 Calculate the square root of the right side: 1.859244504 Break this problem into two subproblems by setting (a + -0.888888889) equal to 1.859244504 and -1.859244504.Subproblem 1
a + -0.888888889 = 1.859244504 Simplifying a + -0.888888889 = 1.859244504 Reorder the terms: -0.888888889 + a = 1.859244504 Solving -0.888888889 + a = 1.859244504 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.888888889' to each side of the equation. -0.888888889 + 0.888888889 + a = 1.859244504 + 0.888888889 Combine like terms: -0.888888889 + 0.888888889 = 0.000000000 0.000000000 + a = 1.859244504 + 0.888888889 a = 1.859244504 + 0.888888889 Combine like terms: 1.859244504 + 0.888888889 = 2.748133393 a = 2.748133393 Simplifying a = 2.748133393Subproblem 2
a + -0.888888889 = -1.859244504 Simplifying a + -0.888888889 = -1.859244504 Reorder the terms: -0.888888889 + a = -1.859244504 Solving -0.888888889 + a = -1.859244504 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.888888889' to each side of the equation. -0.888888889 + 0.888888889 + a = -1.859244504 + 0.888888889 Combine like terms: -0.888888889 + 0.888888889 = 0.000000000 0.000000000 + a = -1.859244504 + 0.888888889 a = -1.859244504 + 0.888888889 Combine like terms: -1.859244504 + 0.888888889 = -0.970355615 a = -0.970355615 Simplifying a = -0.970355615Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.748133393, -0.970355615}
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