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Simplifying -2x + 67 = x2 + -4x + -4 Reorder the terms: 67 + -2x = x2 + -4x + -4 Reorder the terms: 67 + -2x = -4 + -4x + x2 Solving 67 + -2x = -4 + -4x + x2 Solving for variable 'x'. Reorder the terms: 67 + 4 + -2x + 4x + -1x2 = -4 + -4x + x2 + 4 + 4x + -1x2 Combine like terms: 67 + 4 = 71 71 + -2x + 4x + -1x2 = -4 + -4x + x2 + 4 + 4x + -1x2 Combine like terms: -2x + 4x = 2x 71 + 2x + -1x2 = -4 + -4x + x2 + 4 + 4x + -1x2 Reorder the terms: 71 + 2x + -1x2 = -4 + 4 + -4x + 4x + x2 + -1x2 Combine like terms: -4 + 4 = 0 71 + 2x + -1x2 = 0 + -4x + 4x + x2 + -1x2 71 + 2x + -1x2 = -4x + 4x + x2 + -1x2 Combine like terms: -4x + 4x = 0 71 + 2x + -1x2 = 0 + x2 + -1x2 71 + 2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 71 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -71 + -2x + x2 = 0 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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