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Simplifying 3a2 + -5a + -9 = -3 Reorder the terms: -9 + -5a + 3a2 = -3 Solving -9 + -5a + 3a2 = -3 Solving for variable 'a'. Reorder the terms: -9 + 3 + -5a + 3a2 = -3 + 3 Combine like terms: -9 + 3 = -6 -6 + -5a + 3a2 = -3 + 3 Combine like terms: -3 + 3 = 0 -6 + -5a + 3a2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2 + -1.666666667a + a2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -1.666666667a + 2 + a2 = 0 + 2 Reorder the terms: -2 + 2 + -1.666666667a + a2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1.666666667a + a2 = 0 + 2 -1.666666667a + a2 = 0 + 2 Combine like terms: 0 + 2 = 2 -1.666666667a + a2 = 2 The a term is -1.666666667a. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667a + 0.6944444447 + a2 = 2 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667a + a2 = 2 + 0.6944444447 Combine like terms: 2 + 0.6944444447 = 2.6944444447 0.6944444447 + -1.666666667a + a2 = 2.6944444447 Factor a perfect square on the left side: (a + -0.8333333335)(a + -0.8333333335) = 2.6944444447 Calculate the square root of the right side: 1.6414763 Break this problem into two subproblems by setting (a + -0.8333333335) equal to 1.6414763 and -1.6414763.Subproblem 1
a + -0.8333333335 = 1.6414763 Simplifying a + -0.8333333335 = 1.6414763 Reorder the terms: -0.8333333335 + a = 1.6414763 Solving -0.8333333335 + a = 1.6414763 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + a = 1.6414763 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + a = 1.6414763 + 0.8333333335 a = 1.6414763 + 0.8333333335 Combine like terms: 1.6414763 + 0.8333333335 = 2.4748096335 a = 2.4748096335 Simplifying a = 2.4748096335Subproblem 2
a + -0.8333333335 = -1.6414763 Simplifying a + -0.8333333335 = -1.6414763 Reorder the terms: -0.8333333335 + a = -1.6414763 Solving -0.8333333335 + a = -1.6414763 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + a = -1.6414763 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + a = -1.6414763 + 0.8333333335 a = -1.6414763 + 0.8333333335 Combine like terms: -1.6414763 + 0.8333333335 = -0.8081429665 a = -0.8081429665 Simplifying a = -0.8081429665Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.4748096335, -0.8081429665}
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