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Simplifying (-1x2 + 95x + -625) = 0 Reorder the terms: (-625 + 95x + -1x2) = 0 Remove parenthesis around (-625 + 95x + -1x2) -625 + 95x + -1x2 = 0 Solving -625 + 95x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 625 + -95x + x2 = 0 Move the constant term to the right: Add '-625' to each side of the equation. 625 + -95x + -625 + x2 = 0 + -625 Reorder the terms: 625 + -625 + -95x + x2 = 0 + -625 Combine like terms: 625 + -625 = 0 0 + -95x + x2 = 0 + -625 -95x + x2 = 0 + -625 Combine like terms: 0 + -625 = -625 -95x + x2 = -625 The x term is -95x. Take half its coefficient (-47.5). Square it (2256.25) and add it to both sides. Add '2256.25' to each side of the equation. -95x + 2256.25 + x2 = -625 + 2256.25 Reorder the terms: 2256.25 + -95x + x2 = -625 + 2256.25 Combine like terms: -625 + 2256.25 = 1631.25 2256.25 + -95x + x2 = 1631.25 Factor a perfect square on the left side: (x + -47.5)(x + -47.5) = 1631.25 Calculate the square root of the right side: 40.388736054 Break this problem into two subproblems by setting (x + -47.5) equal to 40.388736054 and -40.388736054.Subproblem 1
x + -47.5 = 40.388736054 Simplifying x + -47.5 = 40.388736054 Reorder the terms: -47.5 + x = 40.388736054 Solving -47.5 + x = 40.388736054 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '47.5' to each side of the equation. -47.5 + 47.5 + x = 40.388736054 + 47.5 Combine like terms: -47.5 + 47.5 = 0.0 0.0 + x = 40.388736054 + 47.5 x = 40.388736054 + 47.5 Combine like terms: 40.388736054 + 47.5 = 87.888736054 x = 87.888736054 Simplifying x = 87.888736054Subproblem 2
x + -47.5 = -40.388736054 Simplifying x + -47.5 = -40.388736054 Reorder the terms: -47.5 + x = -40.388736054 Solving -47.5 + x = -40.388736054 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '47.5' to each side of the equation. -47.5 + 47.5 + x = -40.388736054 + 47.5 Combine like terms: -47.5 + 47.5 = 0.0 0.0 + x = -40.388736054 + 47.5 x = -40.388736054 + 47.5 Combine like terms: -40.388736054 + 47.5 = 7.111263946 x = 7.111263946 Simplifying x = 7.111263946Solution
The solution to the problem is based on the solutions from the subproblems. x = {87.888736054, 7.111263946}
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