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Simplifying x2 + -3x + -178 = 0 Reorder the terms: -178 + -3x + x2 = 0 Solving -178 + -3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '178' to each side of the equation. -178 + -3x + 178 + x2 = 0 + 178 Reorder the terms: -178 + 178 + -3x + x2 = 0 + 178 Combine like terms: -178 + 178 = 0 0 + -3x + x2 = 0 + 178 -3x + x2 = 0 + 178 Combine like terms: 0 + 178 = 178 -3x + x2 = 178 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 178 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 178 + 2.25 Combine like terms: 178 + 2.25 = 180.25 2.25 + -3x + x2 = 180.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 180.25 Calculate the square root of the right side: 13.425721582 Break this problem into two subproblems by setting (x + -1.5) equal to 13.425721582 and -13.425721582.Subproblem 1
x + -1.5 = 13.425721582 Simplifying x + -1.5 = 13.425721582 Reorder the terms: -1.5 + x = 13.425721582 Solving -1.5 + x = 13.425721582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 13.425721582 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 13.425721582 + 1.5 x = 13.425721582 + 1.5 Combine like terms: 13.425721582 + 1.5 = 14.925721582 x = 14.925721582 Simplifying x = 14.925721582Subproblem 2
x + -1.5 = -13.425721582 Simplifying x + -1.5 = -13.425721582 Reorder the terms: -1.5 + x = -13.425721582 Solving -1.5 + x = -13.425721582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -13.425721582 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -13.425721582 + 1.5 x = -13.425721582 + 1.5 Combine like terms: -13.425721582 + 1.5 = -11.925721582 x = -11.925721582 Simplifying x = -11.925721582Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.925721582, -11.925721582}
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