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Simplifying a2 + 3a = 49 Reorder the terms: 3a + a2 = 49 Solving 3a + a2 = 49 Solving for variable 'a'. Reorder the terms: -49 + 3a + a2 = 49 + -49 Combine like terms: 49 + -49 = 0 -49 + 3a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + 3a + 49 + a2 = 0 + 49 Reorder the terms: -49 + 49 + 3a + a2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 3a + a2 = 0 + 49 3a + a2 = 0 + 49 Combine like terms: 0 + 49 = 49 3a + a2 = 49 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 = 49 + 2.25 Reorder the terms: 2.25 + 3a + a2 = 49 + 2.25 Combine like terms: 49 + 2.25 = 51.25 2.25 + 3a + a2 = 51.25 Factor a perfect square on the left side: (a + 1.5)(a + 1.5) = 51.25 Calculate the square root of the right side: 7.158910532 Break this problem into two subproblems by setting (a + 1.5) equal to 7.158910532 and -7.158910532.Subproblem 1
a + 1.5 = 7.158910532 Simplifying a + 1.5 = 7.158910532 Reorder the terms: 1.5 + a = 7.158910532 Solving 1.5 + a = 7.158910532 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 = 7.158910532 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + a = 7.158910532 + -1.5 a = 7.158910532 + -1.5 Combine like terms: 7.158910532 + -1.5 = 5.658910532 a = 5.658910532 Simplifying a = 5.658910532Subproblem 2
a + 1.5 = -7.158910532 Simplifying a + 1.5 = -7.158910532 Reorder the terms: 1.5 + a = -7.158910532 Solving 1.5 + a = -7.158910532 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 = -7.158910532 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + a = -7.158910532 + -1.5 a = -7.158910532 + -1.5 Combine like terms: -7.158910532 + -1.5 = -8.658910532 a = -8.658910532 Simplifying a = -8.658910532Solution
The solution to the problem is based on the solutions from the subproblems. a = {5.658910532, -8.658910532}
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