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Simplifying 0 = x2 + -25x + -3000 Reorder the terms: 0 = -3000 + -25x + x2 Solving 0 = -3000 + -25x + x2 Solving for variable 'x'. Combine like terms: 0 + 3000 = 3000 3000 + 25x + -1x2 = -3000 + -25x + x2 + 3000 + 25x + -1x2 Reorder the terms: 3000 + 25x + -1x2 = -3000 + 3000 + -25x + 25x + x2 + -1x2 Combine like terms: -3000 + 3000 = 0 3000 + 25x + -1x2 = 0 + -25x + 25x + x2 + -1x2 3000 + 25x + -1x2 = -25x + 25x + x2 + -1x2 Combine like terms: -25x + 25x = 0 3000 + 25x + -1x2 = 0 + x2 + -1x2 3000 + 25x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 3000 + 25x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3000 + -25x + x2 = 0 Move the constant term to the right: Add '3000' to each side of the equation. -3000 + -25x + 3000 + x2 = 0 + 3000 Reorder the terms: -3000 + 3000 + -25x + x2 = 0 + 3000 Combine like terms: -3000 + 3000 = 0 0 + -25x + x2 = 0 + 3000 -25x + x2 = 0 + 3000 Combine like terms: 0 + 3000 = 3000 -25x + x2 = 3000 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 = 3000 + 156.25 Reorder the terms: 156.25 + -25x + x2 = 3000 + 156.25 Combine like terms: 3000 + 156.25 = 3156.25 156.25 + -25x + x2 = 3156.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 3156.25 Calculate the square root of the right side: 56.180512636 Break this problem into two subproblems by setting (x + -12.5) equal to 56.180512636 and -56.180512636.Subproblem 1
x + -12.5 = 56.180512636 Simplifying x + -12.5 = 56.180512636 Reorder the terms: -12.5 + x = 56.180512636 Solving -12.5 + x = 56.180512636 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 = 56.180512636 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 56.180512636 + 12.5 x = 56.180512636 + 12.5 Combine like terms: 56.180512636 + 12.5 = 68.680512636 x = 68.680512636 Simplifying x = 68.680512636Subproblem 2
x + -12.5 = -56.180512636 Simplifying x + -12.5 = -56.180512636 Reorder the terms: -12.5 + x = -56.180512636 Solving -12.5 + x = -56.180512636 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 = -56.180512636 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -56.180512636 + 12.5 x = -56.180512636 + 12.5 Combine like terms: -56.180512636 + 12.5 = -43.680512636 x = -43.680512636 Simplifying x = -43.680512636Solution
The solution to the problem is based on the solutions from the subproblems. x = {68.680512636, -43.680512636}
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