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Simplifying (4a + -3a2) + (4 + 5a) = 0 Remove parenthesis around (4a + -3a2) 4a + -3a2 + (4 + 5a) = 0 Remove parenthesis around (4 + 5a) 4a + -3a2 + 4 + 5a = 0 Reorder the terms: 4 + 4a + 5a + -3a2 = 0 Combine like terms: 4a + 5a = 9a 4 + 9a + -3a2 = 0 Solving 4 + 9a + -3a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -1.333333333 + -3a + a2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + -3a + 1.333333333 + a2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + -3a + a2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + -3a + a2 = 0 + 1.333333333 -3a + a2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 -3a + a2 = 1.333333333 The a term is -3a. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3a + 2.25 + a2 = 1.333333333 + 2.25 Reorder the terms: 2.25 + -3a + a2 = 1.333333333 + 2.25 Combine like terms: 1.333333333 + 2.25 = 3.583333333 2.25 + -3a + a2 = 3.583333333 Factor a perfect square on the left side: (a + -1.5)(a + -1.5) = 3.583333333 Calculate the square root of the right side: 1.892969449 Break this problem into two subproblems by setting (a + -1.5) equal to 1.892969449 and -1.892969449.Subproblem 1
a + -1.5 = 1.892969449 Simplifying a + -1.5 = 1.892969449 Reorder the terms: -1.5 + a = 1.892969449 Solving -1.5 + a = 1.892969449 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + a = 1.892969449 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + a = 1.892969449 + 1.5 a = 1.892969449 + 1.5 Combine like terms: 1.892969449 + 1.5 = 3.392969449 a = 3.392969449 Simplifying a = 3.392969449Subproblem 2
a + -1.5 = -1.892969449 Simplifying a + -1.5 = -1.892969449 Reorder the terms: -1.5 + a = -1.892969449 Solving -1.5 + a = -1.892969449 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + a = -1.892969449 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + a = -1.892969449 + 1.5 a = -1.892969449 + 1.5 Combine like terms: -1.892969449 + 1.5 = -0.392969449 a = -0.392969449 Simplifying a = -0.392969449Solution
The solution to the problem is based on the solutions from the subproblems. a = {3.392969449, -0.392969449}
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