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Simplifying a(a + -2) + -1(3 + -1a2) = 2 Reorder the terms: a(-2 + a) + -1(3 + -1a2) = 2 (-2 * a + a * a) + -1(3 + -1a2) = 2 (-2a + a2) + -1(3 + -1a2) = 2 -2a + a2 + (3 * -1 + -1a2 * -1) = 2 -2a + a2 + (-3 + 1a2) = 2 Reorder the terms: -3 + -2a + a2 + 1a2 = 2 Combine like terms: a2 + 1a2 = 2a2 -3 + -2a + 2a2 = 2 Solving -3 + -2a + 2a2 = 2 Solving for variable 'a'. Reorder the terms: -3 + -2 + -2a + 2a2 = 2 + -2 Combine like terms: -3 + -2 = -5 -5 + -2a + 2a2 = 2 + -2 Combine like terms: 2 + -2 = 0 -5 + -2a + 2a2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + -1a + a2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -1a + 2.5 + a2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -1a + a2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -1a + a2 = 0 + 2.5 -1a + a2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -1a + a2 = 2.5 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 = 2.5 + 0.25 Reorder the terms: 0.25 + -1a + a2 = 2.5 + 0.25 Combine like terms: 2.5 + 0.25 = 2.75 0.25 + -1a + a2 = 2.75 Factor a perfect square on the left side: (a + -0.5)(a + -0.5) = 2.75 Calculate the square root of the right side: 1.658312395 Break this problem into two subproblems by setting (a + -0.5) equal to 1.658312395 and -1.658312395.Subproblem 1
a + -0.5 = 1.658312395 Simplifying a + -0.5 = 1.658312395 Reorder the terms: -0.5 + a = 1.658312395 Solving -0.5 + a = 1.658312395 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 = 1.658312395 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + a = 1.658312395 + 0.5 a = 1.658312395 + 0.5 Combine like terms: 1.658312395 + 0.5 = 2.158312395 a = 2.158312395 Simplifying a = 2.158312395Subproblem 2
a + -0.5 = -1.658312395 Simplifying a + -0.5 = -1.658312395 Reorder the terms: -0.5 + a = -1.658312395 Solving -0.5 + a = -1.658312395 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 = -1.658312395 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + a = -1.658312395 + 0.5 a = -1.658312395 + 0.5 Combine like terms: -1.658312395 + 0.5 = -1.158312395 a = -1.158312395 Simplifying a = -1.158312395Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.158312395, -1.158312395}
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