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Simplifying x2 + -170x + -600 = 0 Reorder the terms: -600 + -170x + x2 = 0 Solving -600 + -170x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '600' to each side of the equation. -600 + -170x + 600 + x2 = 0 + 600 Reorder the terms: -600 + 600 + -170x + x2 = 0 + 600 Combine like terms: -600 + 600 = 0 0 + -170x + x2 = 0 + 600 -170x + x2 = 0 + 600 Combine like terms: 0 + 600 = 600 -170x + x2 = 600 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 = 600 + 7225 Reorder the terms: 7225 + -170x + x2 = 600 + 7225 Combine like terms: 600 + 7225 = 7825 7225 + -170x + x2 = 7825 Factor a perfect square on the left side: (x + -85)(x + -85) = 7825 Calculate the square root of the right side: 88.459030065 Break this problem into two subproblems by setting (x + -85) equal to 88.459030065 and -88.459030065.Subproblem 1
x + -85 = 88.459030065 Simplifying x + -85 = 88.459030065 Reorder the terms: -85 + x = 88.459030065 Solving -85 + x = 88.459030065 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 = 88.459030065 + 85 Combine like terms: -85 + 85 = 0 0 + x = 88.459030065 + 85 x = 88.459030065 + 85 Combine like terms: 88.459030065 + 85 = 173.459030065 x = 173.459030065 Simplifying x = 173.459030065Subproblem 2
x + -85 = -88.459030065 Simplifying x + -85 = -88.459030065 Reorder the terms: -85 + x = -88.459030065 Solving -85 + x = -88.459030065 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 = -88.459030065 + 85 Combine like terms: -85 + 85 = 0 0 + x = -88.459030065 + 85 x = -88.459030065 + 85 Combine like terms: -88.459030065 + 85 = -3.459030065 x = -3.459030065 Simplifying x = -3.459030065Solution
The solution to the problem is based on the solutions from the subproblems. x = {173.459030065, -3.459030065}
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