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Simplifying a2 + -2a + -224 = 8 Reorder the terms: -224 + -2a + a2 = 8 Solving -224 + -2a + a2 = 8 Solving for variable 'a'. Reorder the terms: -224 + -8 + -2a + a2 = 8 + -8 Combine like terms: -224 + -8 = -232 -232 + -2a + a2 = 8 + -8 Combine like terms: 8 + -8 = 0 -232 + -2a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '232' to each side of the equation. -232 + -2a + 232 + a2 = 0 + 232 Reorder the terms: -232 + 232 + -2a + a2 = 0 + 232 Combine like terms: -232 + 232 = 0 0 + -2a + a2 = 0 + 232 -2a + a2 = 0 + 232 Combine like terms: 0 + 232 = 232 -2a + a2 = 232 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 = 232 + 1 Reorder the terms: 1 + -2a + a2 = 232 + 1 Combine like terms: 232 + 1 = 233 1 + -2a + a2 = 233 Factor a perfect square on the left side: (a + -1)(a + -1) = 233 Calculate the square root of the right side: 15.264337522 Break this problem into two subproblems by setting (a + -1) equal to 15.264337522 and -15.264337522.Subproblem 1
a + -1 = 15.264337522 Simplifying a + -1 = 15.264337522 Reorder the terms: -1 + a = 15.264337522 Solving -1 + a = 15.264337522 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 = 15.264337522 + 1 Combine like terms: -1 + 1 = 0 0 + a = 15.264337522 + 1 a = 15.264337522 + 1 Combine like terms: 15.264337522 + 1 = 16.264337522 a = 16.264337522 Simplifying a = 16.264337522Subproblem 2
a + -1 = -15.264337522 Simplifying a + -1 = -15.264337522 Reorder the terms: -1 + a = -15.264337522 Solving -1 + a = -15.264337522 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 = -15.264337522 + 1 Combine like terms: -1 + 1 = 0 0 + a = -15.264337522 + 1 a = -15.264337522 + 1 Combine like terms: -15.264337522 + 1 = -14.264337522 a = -14.264337522 Simplifying a = -14.264337522Solution
The solution to the problem is based on the solutions from the subproblems. a = {16.264337522, -14.264337522}
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