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Simplifying a2 + -2a + -36 = 0 Reorder the terms: -36 + -2a + a2 = 0 Solving -36 + -2a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -2a + 36 + a2 = 0 + 36 Reorder the terms: -36 + 36 + -2a + a2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -2a + a2 = 0 + 36 -2a + a2 = 0 + 36 Combine like terms: 0 + 36 = 36 -2a + a2 = 36 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 = 36 + 1 Reorder the terms: 1 + -2a + a2 = 36 + 1 Combine like terms: 36 + 1 = 37 1 + -2a + a2 = 37 Factor a perfect square on the left side: (a + -1)(a + -1) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (a + -1) equal to 6.08276253 and -6.08276253.Subproblem 1
a + -1 = 6.08276253 Simplifying a + -1 = 6.08276253 Reorder the terms: -1 + a = 6.08276253 Solving -1 + a = 6.08276253 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 = 6.08276253 + 1 Combine like terms: -1 + 1 = 0 0 + a = 6.08276253 + 1 a = 6.08276253 + 1 Combine like terms: 6.08276253 + 1 = 7.08276253 a = 7.08276253 Simplifying a = 7.08276253Subproblem 2
a + -1 = -6.08276253 Simplifying a + -1 = -6.08276253 Reorder the terms: -1 + a = -6.08276253 Solving -1 + a = -6.08276253 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 = -6.08276253 + 1 Combine like terms: -1 + 1 = 0 0 + a = -6.08276253 + 1 a = -6.08276253 + 1 Combine like terms: -6.08276253 + 1 = -5.08276253 a = -5.08276253 Simplifying a = -5.08276253Solution
The solution to the problem is based on the solutions from the subproblems. a = {7.08276253, -5.08276253}
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