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Simplifying x2 + 43x + -437 = 0 Reorder the terms: -437 + 43x + x2 = 0 Solving -437 + 43x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '437' to each side of the equation. -437 + 43x + 437 + x2 = 0 + 437 Reorder the terms: -437 + 437 + 43x + x2 = 0 + 437 Combine like terms: -437 + 437 = 0 0 + 43x + x2 = 0 + 437 43x + x2 = 0 + 437 Combine like terms: 0 + 437 = 437 43x + x2 = 437 The x term is 43x. Take half its coefficient (21.5). Square it (462.25) and add it to both sides. Add '462.25' to each side of the equation. 43x + 462.25 + x2 = 437 + 462.25 Reorder the terms: 462.25 + 43x + x2 = 437 + 462.25 Combine like terms: 437 + 462.25 = 899.25 462.25 + 43x + x2 = 899.25 Factor a perfect square on the left side: (x + 21.5)(x + 21.5) = 899.25 Calculate the square root of the right side: 29.987497395 Break this problem into two subproblems by setting (x + 21.5) equal to 29.987497395 and -29.987497395.Subproblem 1
x + 21.5 = 29.987497395 Simplifying x + 21.5 = 29.987497395 Reorder the terms: 21.5 + x = 29.987497395 Solving 21.5 + x = 29.987497395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21.5' to each side of the equation. 21.5 + -21.5 + x = 29.987497395 + -21.5 Combine like terms: 21.5 + -21.5 = 0.0 0.0 + x = 29.987497395 + -21.5 x = 29.987497395 + -21.5 Combine like terms: 29.987497395 + -21.5 = 8.487497395 x = 8.487497395 Simplifying x = 8.487497395Subproblem 2
x + 21.5 = -29.987497395 Simplifying x + 21.5 = -29.987497395 Reorder the terms: 21.5 + x = -29.987497395 Solving 21.5 + x = -29.987497395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21.5' to each side of the equation. 21.5 + -21.5 + x = -29.987497395 + -21.5 Combine like terms: 21.5 + -21.5 = 0.0 0.0 + x = -29.987497395 + -21.5 x = -29.987497395 + -21.5 Combine like terms: -29.987497395 + -21.5 = -51.487497395 x = -51.487497395 Simplifying x = -51.487497395Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.487497395, -51.487497395}
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