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Simplifying a2 + 1 = 3a + 15 Reorder the terms: 1 + a2 = 3a + 15 Reorder the terms: 1 + a2 = 15 + 3a Solving 1 + a2 = 15 + 3a Solving for variable 'a'. Reorder the terms: 1 + -15 + -3a + a2 = 15 + 3a + -15 + -3a Combine like terms: 1 + -15 = -14 -14 + -3a + a2 = 15 + 3a + -15 + -3a Reorder the terms: -14 + -3a + a2 = 15 + -15 + 3a + -3a Combine like terms: 15 + -15 = 0 -14 + -3a + a2 = 0 + 3a + -3a -14 + -3a + a2 = 3a + -3a Combine like terms: 3a + -3a = 0 -14 + -3a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + -3a + 14 + a2 = 0 + 14 Reorder the terms: -14 + 14 + -3a + a2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -3a + a2 = 0 + 14 -3a + a2 = 0 + 14 Combine like terms: 0 + 14 = 14 -3a + a2 = 14 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 = 14 + 2.25 Reorder the terms: 2.25 + -3a + a2 = 14 + 2.25 Combine like terms: 14 + 2.25 = 16.25 2.25 + -3a + a2 = 16.25 Factor a perfect square on the left side: (a + -1.5)(a + -1.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (a + -1.5) equal to 4.031128874 and -4.031128874.Subproblem 1
a + -1.5 = 4.031128874 Simplifying a + -1.5 = 4.031128874 Reorder the terms: -1.5 + a = 4.031128874 Solving -1.5 + a = 4.031128874 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 = 4.031128874 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + a = 4.031128874 + 1.5 a = 4.031128874 + 1.5 Combine like terms: 4.031128874 + 1.5 = 5.531128874 a = 5.531128874 Simplifying a = 5.531128874Subproblem 2
a + -1.5 = -4.031128874 Simplifying a + -1.5 = -4.031128874 Reorder the terms: -1.5 + a = -4.031128874 Solving -1.5 + a = -4.031128874 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 = -4.031128874 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + a = -4.031128874 + 1.5 a = -4.031128874 + 1.5 Combine like terms: -4.031128874 + 1.5 = -2.531128874 a = -2.531128874 Simplifying a = -2.531128874Solution
The solution to the problem is based on the solutions from the subproblems. a = {5.531128874, -2.531128874}
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