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Simplifying x2 + -9x + -160 = 0 Reorder the terms: -160 + -9x + x2 = 0 Solving -160 + -9x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '160' to each side of the equation. -160 + -9x + 160 + x2 = 0 + 160 Reorder the terms: -160 + 160 + -9x + x2 = 0 + 160 Combine like terms: -160 + 160 = 0 0 + -9x + x2 = 0 + 160 -9x + x2 = 0 + 160 Combine like terms: 0 + 160 = 160 -9x + x2 = 160 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 160 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 160 + 20.25 Combine like terms: 160 + 20.25 = 180.25 20.25 + -9x + x2 = 180.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 180.25 Calculate the square root of the right side: 13.425721582 Break this problem into two subproblems by setting (x + -4.5) equal to 13.425721582 and -13.425721582.Subproblem 1
x + -4.5 = 13.425721582 Simplifying x + -4.5 = 13.425721582 Reorder the terms: -4.5 + x = 13.425721582 Solving -4.5 + x = 13.425721582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 13.425721582 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 13.425721582 + 4.5 x = 13.425721582 + 4.5 Combine like terms: 13.425721582 + 4.5 = 17.925721582 x = 17.925721582 Simplifying x = 17.925721582Subproblem 2
x + -4.5 = -13.425721582 Simplifying x + -4.5 = -13.425721582 Reorder the terms: -4.5 + x = -13.425721582 Solving -4.5 + x = -13.425721582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -13.425721582 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -13.425721582 + 4.5 x = -13.425721582 + 4.5 Combine like terms: -13.425721582 + 4.5 = -8.925721582 x = -8.925721582 Simplifying x = -8.925721582Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.925721582, -8.925721582}
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