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Simplifying a2 + 2a + -23 = 0 Reorder the terms: -23 + 2a + a2 = 0 Solving -23 + 2a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + 2a + 23 + a2 = 0 + 23 Reorder the terms: -23 + 23 + 2a + a2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + 2a + a2 = 0 + 23 2a + a2 = 0 + 23 Combine like terms: 0 + 23 = 23 2a + a2 = 23 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 = 23 + 1 Reorder the terms: 1 + 2a + a2 = 23 + 1 Combine like terms: 23 + 1 = 24 1 + 2a + a2 = 24 Factor a perfect square on the left side: (a + 1)(a + 1) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (a + 1) equal to 4.898979486 and -4.898979486.Subproblem 1
a + 1 = 4.898979486 Simplifying a + 1 = 4.898979486 Reorder the terms: 1 + a = 4.898979486 Solving 1 + a = 4.898979486 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 = 4.898979486 + -1 Combine like terms: 1 + -1 = 0 0 + a = 4.898979486 + -1 a = 4.898979486 + -1 Combine like terms: 4.898979486 + -1 = 3.898979486 a = 3.898979486 Simplifying a = 3.898979486Subproblem 2
a + 1 = -4.898979486 Simplifying a + 1 = -4.898979486 Reorder the terms: 1 + a = -4.898979486 Solving 1 + a = -4.898979486 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 = -4.898979486 + -1 Combine like terms: 1 + -1 = 0 0 + a = -4.898979486 + -1 a = -4.898979486 + -1 Combine like terms: -4.898979486 + -1 = -5.898979486 a = -5.898979486 Simplifying a = -5.898979486Solution
The solution to the problem is based on the solutions from the subproblems. a = {3.898979486, -5.898979486}
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