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Simplifying (a + -3)(a + 1) = 2 Reorder the terms: (-3 + a)(a + 1) = 2 Reorder the terms: (-3 + a)(1 + a) = 2 Multiply (-3 + a) * (1 + a) (-3(1 + a) + a(1 + a)) = 2 ((1 * -3 + a * -3) + a(1 + a)) = 2 ((-3 + -3a) + a(1 + a)) = 2 (-3 + -3a + (1 * a + a * a)) = 2 (-3 + -3a + (1a + a2)) = 2 Combine like terms: -3a + 1a = -2a (-3 + -2a + a2) = 2 Solving -3 + -2a + a2 = 2 Solving for variable 'a'. Reorder the terms: -3 + -2 + -2a + a2 = 2 + -2 Combine like terms: -3 + -2 = -5 -5 + -2a + a2 = 2 + -2 Combine like terms: 2 + -2 = 0 -5 + -2a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -2a + 5 + a2 = 0 + 5 Reorder the terms: -5 + 5 + -2a + a2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2a + a2 = 0 + 5 -2a + a2 = 0 + 5 Combine like terms: 0 + 5 = 5 -2a + a2 = 5 The a term is -2a. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2a + 1 + a2 = 5 + 1 Reorder the terms: 1 + -2a + a2 = 5 + 1 Combine like terms: 5 + 1 = 6 1 + -2a + a2 = 6 Factor a perfect square on the left side: (a + -1)(a + -1) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (a + -1) equal to 2.449489743 and -2.449489743.Subproblem 1
a + -1 = 2.449489743 Simplifying a + -1 = 2.449489743 Reorder the terms: -1 + a = 2.449489743 Solving -1 + a = 2.449489743 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + a = 2.449489743 + 1 Combine like terms: -1 + 1 = 0 0 + a = 2.449489743 + 1 a = 2.449489743 + 1 Combine like terms: 2.449489743 + 1 = 3.449489743 a = 3.449489743 Simplifying a = 3.449489743Subproblem 2
a + -1 = -2.449489743 Simplifying a + -1 = -2.449489743 Reorder the terms: -1 + a = -2.449489743 Solving -1 + a = -2.449489743 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + a = -2.449489743 + 1 Combine like terms: -1 + 1 = 0 0 + a = -2.449489743 + 1 a = -2.449489743 + 1 Combine like terms: -2.449489743 + 1 = -1.449489743 a = -1.449489743 Simplifying a = -1.449489743Solution
The solution to the problem is based on the solutions from the subproblems. a = {3.449489743, -1.449489743}
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