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Simplifying a2 + -2a + -19 = 0 Reorder the terms: -19 + -2a + a2 = 0 Solving -19 + -2a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + -2a + 19 + a2 = 0 + 19 Reorder the terms: -19 + 19 + -2a + a2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -2a + a2 = 0 + 19 -2a + a2 = 0 + 19 Combine like terms: 0 + 19 = 19 -2a + a2 = 19 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 = 19 + 1 Reorder the terms: 1 + -2a + a2 = 19 + 1 Combine like terms: 19 + 1 = 20 1 + -2a + a2 = 20 Factor a perfect square on the left side: (a + -1)(a + -1) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (a + -1) equal to 4.472135955 and -4.472135955.Subproblem 1
a + -1 = 4.472135955 Simplifying a + -1 = 4.472135955 Reorder the terms: -1 + a = 4.472135955 Solving -1 + a = 4.472135955 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 = 4.472135955 + 1 Combine like terms: -1 + 1 = 0 0 + a = 4.472135955 + 1 a = 4.472135955 + 1 Combine like terms: 4.472135955 + 1 = 5.472135955 a = 5.472135955 Simplifying a = 5.472135955Subproblem 2
a + -1 = -4.472135955 Simplifying a + -1 = -4.472135955 Reorder the terms: -1 + a = -4.472135955 Solving -1 + a = -4.472135955 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 = -4.472135955 + 1 Combine like terms: -1 + 1 = 0 0 + a = -4.472135955 + 1 a = -4.472135955 + 1 Combine like terms: -4.472135955 + 1 = -3.472135955 a = -3.472135955 Simplifying a = -3.472135955Solution
The solution to the problem is based on the solutions from the subproblems. a = {5.472135955, -3.472135955}
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