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Simplifying (a + -2)(a + 1) = 6 Reorder the terms: (-2 + a)(a + 1) = 6 Reorder the terms: (-2 + a)(1 + a) = 6 Multiply (-2 + a) * (1 + a) (-2(1 + a) + a(1 + a)) = 6 ((1 * -2 + a * -2) + a(1 + a)) = 6 ((-2 + -2a) + a(1 + a)) = 6 (-2 + -2a + (1 * a + a * a)) = 6 (-2 + -2a + (1a + a2)) = 6 Combine like terms: -2a + 1a = -1a (-2 + -1a + a2) = 6 Solving -2 + -1a + a2 = 6 Solving for variable 'a'. Reorder the terms: -2 + -6 + -1a + a2 = 6 + -6 Combine like terms: -2 + -6 = -8 -8 + -1a + a2 = 6 + -6 Combine like terms: 6 + -6 = 0 -8 + -1a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -1a + 8 + a2 = 0 + 8 Reorder the terms: -8 + 8 + -1a + a2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1a + a2 = 0 + 8 -1a + a2 = 0 + 8 Combine like terms: 0 + 8 = 8 -1a + a2 = 8 The a term is -1a. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1a + 0.25 + a2 = 8 + 0.25 Reorder the terms: 0.25 + -1a + a2 = 8 + 0.25 Combine like terms: 8 + 0.25 = 8.25 0.25 + -1a + a2 = 8.25 Factor a perfect square on the left side: (a + -0.5)(a + -0.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (a + -0.5) equal to 2.872281323 and -2.872281323.Subproblem 1
a + -0.5 = 2.872281323 Simplifying a + -0.5 = 2.872281323 Reorder the terms: -0.5 + a = 2.872281323 Solving -0.5 + a = 2.872281323 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + a = 2.872281323 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + a = 2.872281323 + 0.5 a = 2.872281323 + 0.5 Combine like terms: 2.872281323 + 0.5 = 3.372281323 a = 3.372281323 Simplifying a = 3.372281323Subproblem 2
a + -0.5 = -2.872281323 Simplifying a + -0.5 = -2.872281323 Reorder the terms: -0.5 + a = -2.872281323 Solving -0.5 + a = -2.872281323 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + a = -2.872281323 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + a = -2.872281323 + 0.5 a = -2.872281323 + 0.5 Combine like terms: -2.872281323 + 0.5 = -2.372281323 a = -2.372281323 Simplifying a = -2.372281323Solution
The solution to the problem is based on the solutions from the subproblems. a = {3.372281323, -2.372281323}
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