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Simplifying x2 + -175 = x Reorder the terms: -175 + x2 = x Solving -175 + x2 = x Solving for variable 'x'. Reorder the terms: -175 + -1x + x2 = x + -1x Combine like terms: x + -1x = 0 -175 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '175' to each side of the equation. -175 + -1x + 175 + x2 = 0 + 175 Reorder the terms: -175 + 175 + -1x + x2 = 0 + 175 Combine like terms: -175 + 175 = 0 0 + -1x + x2 = 0 + 175 -1x + x2 = 0 + 175 Combine like terms: 0 + 175 = 175 -1x + x2 = 175 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 175 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 175 + 0.25 Combine like terms: 175 + 0.25 = 175.25 0.25 + -1x + x2 = 175.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 175.25 Calculate the square root of the right side: 13.238202295 Break this problem into two subproblems by setting (x + -0.5) equal to 13.238202295 and -13.238202295.Subproblem 1
x + -0.5 = 13.238202295 Simplifying x + -0.5 = 13.238202295 Reorder the terms: -0.5 + x = 13.238202295 Solving -0.5 + x = 13.238202295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 13.238202295 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 13.238202295 + 0.5 x = 13.238202295 + 0.5 Combine like terms: 13.238202295 + 0.5 = 13.738202295 x = 13.738202295 Simplifying x = 13.738202295Subproblem 2
x + -0.5 = -13.238202295 Simplifying x + -0.5 = -13.238202295 Reorder the terms: -0.5 + x = -13.238202295 Solving -0.5 + x = -13.238202295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -13.238202295 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -13.238202295 + 0.5 x = -13.238202295 + 0.5 Combine like terms: -13.238202295 + 0.5 = -12.738202295 x = -12.738202295 Simplifying x = -12.738202295Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.738202295, -12.738202295}
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