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Simplifying x2 + 80x + 1 = 0 Reorder the terms: 1 + 80x + x2 = 0 Solving 1 + 80x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 80x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 80x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 80x + x2 = 0 + -1 80x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 80x + x2 = -1 The x term is 80x. Take half its coefficient (40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. 80x + 1600 + x2 = -1 + 1600 Reorder the terms: 1600 + 80x + x2 = -1 + 1600 Combine like terms: -1 + 1600 = 1599 1600 + 80x + x2 = 1599 Factor a perfect square on the left side: (x + 40)(x + 40) = 1599 Calculate the square root of the right side: 39.987498046 Break this problem into two subproblems by setting (x + 40) equal to 39.987498046 and -39.987498046.Subproblem 1
x + 40 = 39.987498046 Simplifying x + 40 = 39.987498046 Reorder the terms: 40 + x = 39.987498046 Solving 40 + x = 39.987498046 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + x = 39.987498046 + -40 Combine like terms: 40 + -40 = 0 0 + x = 39.987498046 + -40 x = 39.987498046 + -40 Combine like terms: 39.987498046 + -40 = -0.012501954 x = -0.012501954 Simplifying x = -0.012501954Subproblem 2
x + 40 = -39.987498046 Simplifying x + 40 = -39.987498046 Reorder the terms: 40 + x = -39.987498046 Solving 40 + x = -39.987498046 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + x = -39.987498046 + -40 Combine like terms: 40 + -40 = 0 0 + x = -39.987498046 + -40 x = -39.987498046 + -40 Combine like terms: -39.987498046 + -40 = -79.987498046 x = -79.987498046 Simplifying x = -79.987498046Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.012501954, -79.987498046}
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