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Simplifying x2 + -25x + -24 = 0 Reorder the terms: -24 + -25x + x2 = 0 Solving -24 + -25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + -25x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + -25x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -25x + x2 = 0 + 24 -25x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 -25x + x2 = 24 The x term is -25x. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25x + 156.25 + x2 = 24 + 156.25 Reorder the terms: 156.25 + -25x + x2 = 24 + 156.25 Combine like terms: 24 + 156.25 = 180.25 156.25 + -25x + x2 = 180.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 180.25 Calculate the square root of the right side: 13.425721582 Break this problem into two subproblems by setting (x + -12.5) equal to 13.425721582 and -13.425721582.Subproblem 1
x + -12.5 = 13.425721582 Simplifying x + -12.5 = 13.425721582 Reorder the terms: -12.5 + x = 13.425721582 Solving -12.5 + x = 13.425721582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = 13.425721582 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 13.425721582 + 12.5 x = 13.425721582 + 12.5 Combine like terms: 13.425721582 + 12.5 = 25.925721582 x = 25.925721582 Simplifying x = 25.925721582Subproblem 2
x + -12.5 = -13.425721582 Simplifying x + -12.5 = -13.425721582 Reorder the terms: -12.5 + x = -13.425721582 Solving -12.5 + x = -13.425721582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = -13.425721582 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -13.425721582 + 12.5 x = -13.425721582 + 12.5 Combine like terms: -13.425721582 + 12.5 = -0.925721582 x = -0.925721582 Simplifying x = -0.925721582Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.925721582, -0.925721582}
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