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Simplifying a2 + 3a + -29 = 0 Reorder the terms: -29 + 3a + a2 = 0 Solving -29 + 3a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + 3a + 29 + a2 = 0 + 29 Reorder the terms: -29 + 29 + 3a + a2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + 3a + a2 = 0 + 29 3a + a2 = 0 + 29 Combine like terms: 0 + 29 = 29 3a + a2 = 29 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 = 29 + 2.25 Reorder the terms: 2.25 + 3a + a2 = 29 + 2.25 Combine like terms: 29 + 2.25 = 31.25 2.25 + 3a + a2 = 31.25 Factor a perfect square on the left side: (a + 1.5)(a + 1.5) = 31.25 Calculate the square root of the right side: 5.590169944 Break this problem into two subproblems by setting (a + 1.5) equal to 5.590169944 and -5.590169944.Subproblem 1
a + 1.5 = 5.590169944 Simplifying a + 1.5 = 5.590169944 Reorder the terms: 1.5 + a = 5.590169944 Solving 1.5 + a = 5.590169944 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 = 5.590169944 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + a = 5.590169944 + -1.5 a = 5.590169944 + -1.5 Combine like terms: 5.590169944 + -1.5 = 4.090169944 a = 4.090169944 Simplifying a = 4.090169944Subproblem 2
a + 1.5 = -5.590169944 Simplifying a + 1.5 = -5.590169944 Reorder the terms: 1.5 + a = -5.590169944 Solving 1.5 + a = -5.590169944 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 = -5.590169944 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + a = -5.590169944 + -1.5 a = -5.590169944 + -1.5 Combine like terms: -5.590169944 + -1.5 = -7.090169944 a = -7.090169944 Simplifying a = -7.090169944Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.090169944, -7.090169944}
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