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Simplifying 9a2 + -24 = -11a Reorder the terms: -24 + 9a2 = -11a Solving -24 + 9a2 = -11a Solving for variable 'a'. Reorder the terms: -24 + 11a + 9a2 = -11a + 11a Combine like terms: -11a + 11a = 0 -24 + 11a + 9a2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.666666667 + 1.222222222a + a2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + 1.222222222a + 2.666666667 + a2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + 1.222222222a + a2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + 1.222222222a + a2 = 0 + 2.666666667 1.222222222a + a2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 1.222222222a + a2 = 2.666666667 The a term is 1.222222222a. Take half its coefficient (0.611111111). Square it (0.3734567900) and add it to both sides. Add '0.3734567900' to each side of the equation. 1.222222222a + 0.3734567900 + a2 = 2.666666667 + 0.3734567900 Reorder the terms: 0.3734567900 + 1.222222222a + a2 = 2.666666667 + 0.3734567900 Combine like terms: 2.666666667 + 0.3734567900 = 3.040123457 0.3734567900 + 1.222222222a + a2 = 3.040123457 Factor a perfect square on the left side: (a + 0.611111111)(a + 0.611111111) = 3.040123457 Calculate the square root of the right side: 1.743594981 Break this problem into two subproblems by setting (a + 0.611111111) equal to 1.743594981 and -1.743594981.Subproblem 1
a + 0.611111111 = 1.743594981 Simplifying a + 0.611111111 = 1.743594981 Reorder the terms: 0.611111111 + a = 1.743594981 Solving 0.611111111 + a = 1.743594981 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.611111111' to each side of the equation. 0.611111111 + -0.611111111 + a = 1.743594981 + -0.611111111 Combine like terms: 0.611111111 + -0.611111111 = 0.000000000 0.000000000 + a = 1.743594981 + -0.611111111 a = 1.743594981 + -0.611111111 Combine like terms: 1.743594981 + -0.611111111 = 1.13248387 a = 1.13248387 Simplifying a = 1.13248387Subproblem 2
a + 0.611111111 = -1.743594981 Simplifying a + 0.611111111 = -1.743594981 Reorder the terms: 0.611111111 + a = -1.743594981 Solving 0.611111111 + a = -1.743594981 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.611111111' to each side of the equation. 0.611111111 + -0.611111111 + a = -1.743594981 + -0.611111111 Combine like terms: 0.611111111 + -0.611111111 = 0.000000000 0.000000000 + a = -1.743594981 + -0.611111111 a = -1.743594981 + -0.611111111 Combine like terms: -1.743594981 + -0.611111111 = -2.354706092 a = -2.354706092 Simplifying a = -2.354706092Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.13248387, -2.354706092}
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