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Simplifying x2 + 170x + -1114 = 0 Reorder the terms: -1114 + 170x + x2 = 0 Solving -1114 + 170x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1114' to each side of the equation. -1114 + 170x + 1114 + x2 = 0 + 1114 Reorder the terms: -1114 + 1114 + 170x + x2 = 0 + 1114 Combine like terms: -1114 + 1114 = 0 0 + 170x + x2 = 0 + 1114 170x + x2 = 0 + 1114 Combine like terms: 0 + 1114 = 1114 170x + x2 = 1114 The x term is 170x. Take half its coefficient (85). Square it (7225) and add it to both sides. Add '7225' to each side of the equation. 170x + 7225 + x2 = 1114 + 7225 Reorder the terms: 7225 + 170x + x2 = 1114 + 7225 Combine like terms: 1114 + 7225 = 8339 7225 + 170x + x2 = 8339 Factor a perfect square on the left side: (x + 85)(x + 85) = 8339 Calculate the square root of the right side: 91.318125255 Break this problem into two subproblems by setting (x + 85) equal to 91.318125255 and -91.318125255.Subproblem 1
x + 85 = 91.318125255 Simplifying x + 85 = 91.318125255 Reorder the terms: 85 + x = 91.318125255 Solving 85 + x = 91.318125255 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-85' to each side of the equation. 85 + -85 + x = 91.318125255 + -85 Combine like terms: 85 + -85 = 0 0 + x = 91.318125255 + -85 x = 91.318125255 + -85 Combine like terms: 91.318125255 + -85 = 6.318125255 x = 6.318125255 Simplifying x = 6.318125255Subproblem 2
x + 85 = -91.318125255 Simplifying x + 85 = -91.318125255 Reorder the terms: 85 + x = -91.318125255 Solving 85 + x = -91.318125255 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-85' to each side of the equation. 85 + -85 + x = -91.318125255 + -85 Combine like terms: 85 + -85 = 0 0 + x = -91.318125255 + -85 x = -91.318125255 + -85 Combine like terms: -91.318125255 + -85 = -176.318125255 x = -176.318125255 Simplifying x = -176.318125255Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.318125255, -176.318125255}
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