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Simplifying -0.5x2 + -12.5x + 25 = -200 Reorder the terms: 25 + -12.5x + -0.5x2 = -200 Solving 25 + -12.5x + -0.5x2 = -200 Solving for variable 'x'. Reorder the terms: 25 + 200 + -12.5x + -0.5x2 = -200 + 200 Combine like terms: 25 + 200 = 225 225 + -12.5x + -0.5x2 = -200 + 200 Combine like terms: -200 + 200 = 0 225 + -12.5x + -0.5x2 = 0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -450 + 25x + x2 = 0 Move the constant term to the right: Add '450' to each side of the equation. -450 + 25x + 450 + x2 = 0 + 450 Reorder the terms: -450 + 450 + 25x + x2 = 0 + 450 Combine like terms: -450 + 450 = 0 0 + 25x + x2 = 0 + 450 25x + x2 = 0 + 450 Combine like terms: 0 + 450 = 450 25x + x2 = 450 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 = 450 + 156.25 Reorder the terms: 156.25 + 25x + x2 = 450 + 156.25 Combine like terms: 450 + 156.25 = 606.25 156.25 + 25x + x2 = 606.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 606.25 Calculate the square root of the right side: 24.622144504 Break this problem into two subproblems by setting (x + 12.5) equal to 24.622144504 and -24.622144504.Subproblem 1
x + 12.5 = 24.622144504 Simplifying x + 12.5 = 24.622144504 Reorder the terms: 12.5 + x = 24.622144504 Solving 12.5 + x = 24.622144504 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 = 24.622144504 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 24.622144504 + -12.5 x = 24.622144504 + -12.5 Combine like terms: 24.622144504 + -12.5 = 12.122144504 x = 12.122144504 Simplifying x = 12.122144504Subproblem 2
x + 12.5 = -24.622144504 Simplifying x + 12.5 = -24.622144504 Reorder the terms: 12.5 + x = -24.622144504 Solving 12.5 + x = -24.622144504 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 = -24.622144504 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -24.622144504 + -12.5 x = -24.622144504 + -12.5 Combine like terms: -24.622144504 + -12.5 = -37.122144504 x = -37.122144504 Simplifying x = -37.122144504Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.122144504, -37.122144504}
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