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Simplifying (5a2 + 3a + -1) + (a + -9) = 0 Reorder the terms: (-1 + 3a + 5a2) + (a + -9) = 0 Remove parenthesis around (-1 + 3a + 5a2) -1 + 3a + 5a2 + (a + -9) = 0 Reorder the terms: -1 + 3a + 5a2 + (-9 + a) = 0 Remove parenthesis around (-9 + a) -1 + 3a + 5a2 + -9 + a = 0 Reorder the terms: -1 + -9 + 3a + a + 5a2 = 0 Combine like terms: -1 + -9 = -10 -10 + 3a + a + 5a2 = 0 Combine like terms: 3a + a = 4a -10 + 4a + 5a2 = 0 Solving -10 + 4a + 5a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2 + 0.8a + a2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 0.8a + 2 + a2 = 0 + 2 Reorder the terms: -2 + 2 + 0.8a + a2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 0.8a + a2 = 0 + 2 0.8a + a2 = 0 + 2 Combine like terms: 0 + 2 = 2 0.8a + a2 = 2 The a term is 0.8a. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8a + 0.16 + a2 = 2 + 0.16 Reorder the terms: 0.16 + 0.8a + a2 = 2 + 0.16 Combine like terms: 2 + 0.16 = 2.16 0.16 + 0.8a + a2 = 2.16 Factor a perfect square on the left side: (a + 0.4)(a + 0.4) = 2.16 Calculate the square root of the right side: 1.469693846 Break this problem into two subproblems by setting (a + 0.4) equal to 1.469693846 and -1.469693846.Subproblem 1
a + 0.4 = 1.469693846 Simplifying a + 0.4 = 1.469693846 Reorder the terms: 0.4 + a = 1.469693846 Solving 0.4 + a = 1.469693846 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + a = 1.469693846 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + a = 1.469693846 + -0.4 a = 1.469693846 + -0.4 Combine like terms: 1.469693846 + -0.4 = 1.069693846 a = 1.069693846 Simplifying a = 1.069693846Subproblem 2
a + 0.4 = -1.469693846 Simplifying a + 0.4 = -1.469693846 Reorder the terms: 0.4 + a = -1.469693846 Solving 0.4 + a = -1.469693846 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + a = -1.469693846 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + a = -1.469693846 + -0.4 a = -1.469693846 + -0.4 Combine like terms: -1.469693846 + -0.4 = -1.869693846 a = -1.869693846 Simplifying a = -1.869693846Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.069693846, -1.869693846}
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