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Simplifying x2 + -170x + -172 = 0 Reorder the terms: -172 + -170x + x2 = 0 Solving -172 + -170x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '172' to each side of the equation. -172 + -170x + 172 + x2 = 0 + 172 Reorder the terms: -172 + 172 + -170x + x2 = 0 + 172 Combine like terms: -172 + 172 = 0 0 + -170x + x2 = 0 + 172 -170x + x2 = 0 + 172 Combine like terms: 0 + 172 = 172 -170x + x2 = 172 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 = 172 + 7225 Reorder the terms: 7225 + -170x + x2 = 172 + 7225 Combine like terms: 172 + 7225 = 7397 7225 + -170x + x2 = 7397 Factor a perfect square on the left side: (x + -85)(x + -85) = 7397 Calculate the square root of the right side: 86.005813757 Break this problem into two subproblems by setting (x + -85) equal to 86.005813757 and -86.005813757.Subproblem 1
x + -85 = 86.005813757 Simplifying x + -85 = 86.005813757 Reorder the terms: -85 + x = 86.005813757 Solving -85 + x = 86.005813757 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 = 86.005813757 + 85 Combine like terms: -85 + 85 = 0 0 + x = 86.005813757 + 85 x = 86.005813757 + 85 Combine like terms: 86.005813757 + 85 = 171.005813757 x = 171.005813757 Simplifying x = 171.005813757Subproblem 2
x + -85 = -86.005813757 Simplifying x + -85 = -86.005813757 Reorder the terms: -85 + x = -86.005813757 Solving -85 + x = -86.005813757 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 = -86.005813757 + 85 Combine like terms: -85 + 85 = 0 0 + x = -86.005813757 + 85 x = -86.005813757 + 85 Combine like terms: -86.005813757 + 85 = -1.005813757 x = -1.005813757 Simplifying x = -1.005813757Solution
The solution to the problem is based on the solutions from the subproblems. x = {171.005813757, -1.005813757}
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