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Simplifying x2 + -2x + -71 = 0 Reorder the terms: -71 + -2x + x2 = 0 Solving -71 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '71' to each side of the equation. -71 + -2x + 71 + x2 = 0 + 71 Reorder the terms: -71 + 71 + -2x + x2 = 0 + 71 Combine like terms: -71 + 71 = 0 0 + -2x + x2 = 0 + 71 -2x + x2 = 0 + 71 Combine like terms: 0 + 71 = 71 -2x + x2 = 71 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 71 + 1 Reorder the terms: 1 + -2x + x2 = 71 + 1 Combine like terms: 71 + 1 = 72 1 + -2x + x2 = 72 Factor a perfect square on the left side: (x + -1)(x + -1) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (x + -1) equal to 8.485281374 and -8.485281374.Subproblem 1
x + -1 = 8.485281374 Simplifying x + -1 = 8.485281374 Reorder the terms: -1 + x = 8.485281374 Solving -1 + x = 8.485281374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 8.485281374 + 1 Combine like terms: -1 + 1 = 0 0 + x = 8.485281374 + 1 x = 8.485281374 + 1 Combine like terms: 8.485281374 + 1 = 9.485281374 x = 9.485281374 Simplifying x = 9.485281374Subproblem 2
x + -1 = -8.485281374 Simplifying x + -1 = -8.485281374 Reorder the terms: -1 + x = -8.485281374 Solving -1 + x = -8.485281374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -8.485281374 + 1 Combine like terms: -1 + 1 = 0 0 + x = -8.485281374 + 1 x = -8.485281374 + 1 Combine like terms: -8.485281374 + 1 = -7.485281374 x = -7.485281374 Simplifying x = -7.485281374Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.485281374, -7.485281374}
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