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Simplifying x2 + 46x + 383 = 0 Reorder the terms: 383 + 46x + x2 = 0 Solving 383 + 46x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-383' to each side of the equation. 383 + 46x + -383 + x2 = 0 + -383 Reorder the terms: 383 + -383 + 46x + x2 = 0 + -383 Combine like terms: 383 + -383 = 0 0 + 46x + x2 = 0 + -383 46x + x2 = 0 + -383 Combine like terms: 0 + -383 = -383 46x + x2 = -383 The x term is 46x. Take half its coefficient (23). Square it (529) and add it to both sides. Add '529' to each side of the equation. 46x + 529 + x2 = -383 + 529 Reorder the terms: 529 + 46x + x2 = -383 + 529 Combine like terms: -383 + 529 = 146 529 + 46x + x2 = 146 Factor a perfect square on the left side: (x + 23)(x + 23) = 146 Calculate the square root of the right side: 12.083045974 Break this problem into two subproblems by setting (x + 23) equal to 12.083045974 and -12.083045974.Subproblem 1
x + 23 = 12.083045974 Simplifying x + 23 = 12.083045974 Reorder the terms: 23 + x = 12.083045974 Solving 23 + x = 12.083045974 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + x = 12.083045974 + -23 Combine like terms: 23 + -23 = 0 0 + x = 12.083045974 + -23 x = 12.083045974 + -23 Combine like terms: 12.083045974 + -23 = -10.916954026 x = -10.916954026 Simplifying x = -10.916954026Subproblem 2
x + 23 = -12.083045974 Simplifying x + 23 = -12.083045974 Reorder the terms: 23 + x = -12.083045974 Solving 23 + x = -12.083045974 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + x = -12.083045974 + -23 Combine like terms: 23 + -23 = 0 0 + x = -12.083045974 + -23 x = -12.083045974 + -23 Combine like terms: -12.083045974 + -23 = -35.083045974 x = -35.083045974 Simplifying x = -35.083045974Solution
The solution to the problem is based on the solutions from the subproblems. x = {-10.916954026, -35.083045974}
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