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Simplifying a2 + 3a + -35 = 0 Reorder the terms: -35 + 3a + a2 = 0 Solving -35 + 3a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + 3a + 35 + a2 = 0 + 35 Reorder the terms: -35 + 35 + 3a + a2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + 3a + a2 = 0 + 35 3a + a2 = 0 + 35 Combine like terms: 0 + 35 = 35 3a + a2 = 35 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 = 35 + 2.25 Reorder the terms: 2.25 + 3a + a2 = 35 + 2.25 Combine like terms: 35 + 2.25 = 37.25 2.25 + 3a + a2 = 37.25 Factor a perfect square on the left side: (a + 1.5)(a + 1.5) = 37.25 Calculate the square root of the right side: 6.103277808 Break this problem into two subproblems by setting (a + 1.5) equal to 6.103277808 and -6.103277808.Subproblem 1
a + 1.5 = 6.103277808 Simplifying a + 1.5 = 6.103277808 Reorder the terms: 1.5 + a = 6.103277808 Solving 1.5 + a = 6.103277808 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 = 6.103277808 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + a = 6.103277808 + -1.5 a = 6.103277808 + -1.5 Combine like terms: 6.103277808 + -1.5 = 4.603277808 a = 4.603277808 Simplifying a = 4.603277808Subproblem 2
a + 1.5 = -6.103277808 Simplifying a + 1.5 = -6.103277808 Reorder the terms: 1.5 + a = -6.103277808 Solving 1.5 + a = -6.103277808 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 = -6.103277808 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + a = -6.103277808 + -1.5 a = -6.103277808 + -1.5 Combine like terms: -6.103277808 + -1.5 = -7.603277808 a = -7.603277808 Simplifying a = -7.603277808Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.603277808, -7.603277808}
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