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Simplifying a(a + -2) = (a + 5) + -1(a + 3) Reorder the terms: a(-2 + a) = (a + 5) + -1(a + 3) (-2 * a + a * a) = (a + 5) + -1(a + 3) (-2a + a2) = (a + 5) + -1(a + 3) Reorder the terms: -2a + a2 = (5 + a) + -1(a + 3) Remove parenthesis around (5 + a) -2a + a2 = 5 + a + -1(a + 3) Reorder the terms: -2a + a2 = 5 + a + -1(3 + a) -2a + a2 = 5 + a + (3 * -1 + a * -1) -2a + a2 = 5 + a + (-3 + -1a) Reorder the terms: -2a + a2 = 5 + -3 + a + -1a Combine like terms: 5 + -3 = 2 -2a + a2 = 2 + a + -1a Combine like terms: a + -1a = 0 -2a + a2 = 2 + 0 -2a + a2 = 2 Solving -2a + a2 = 2 Solving for variable 'a'. Reorder the terms: -2 + -2a + a2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -2a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -2a + 2 + a2 = 0 + 2 Reorder the terms: -2 + 2 + -2a + a2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -2a + a2 = 0 + 2 -2a + a2 = 0 + 2 Combine like terms: 0 + 2 = 2 -2a + a2 = 2 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 = 2 + 1 Reorder the terms: 1 + -2a + a2 = 2 + 1 Combine like terms: 2 + 1 = 3 1 + -2a + a2 = 3 Factor a perfect square on the left side: (a + -1)(a + -1) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (a + -1) equal to 1.732050808 and -1.732050808.Subproblem 1
a + -1 = 1.732050808 Simplifying a + -1 = 1.732050808 Reorder the terms: -1 + a = 1.732050808 Solving -1 + a = 1.732050808 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 = 1.732050808 + 1 Combine like terms: -1 + 1 = 0 0 + a = 1.732050808 + 1 a = 1.732050808 + 1 Combine like terms: 1.732050808 + 1 = 2.732050808 a = 2.732050808 Simplifying a = 2.732050808Subproblem 2
a + -1 = -1.732050808 Simplifying a + -1 = -1.732050808 Reorder the terms: -1 + a = -1.732050808 Solving -1 + a = -1.732050808 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 = -1.732050808 + 1 Combine like terms: -1 + 1 = 0 0 + a = -1.732050808 + 1 a = -1.732050808 + 1 Combine like terms: -1.732050808 + 1 = -0.732050808 a = -0.732050808 Simplifying a = -0.732050808Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.732050808, -0.732050808}
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