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Simplifying x = -0.001x2 + 2.45x + -525 Reorder the terms: x = -525 + 2.45x + -0.001x2 Solving x = -525 + 2.45x + -0.001x2 Solving for variable 'x'. Reorder the terms: 525 + x + -2.45x + 0.001x2 = -525 + 2.45x + -0.001x2 + 525 + -2.45x + 0.001x2 Combine like terms: x + -2.45x = -1.45x 525 + -1.45x + 0.001x2 = -525 + 2.45x + -0.001x2 + 525 + -2.45x + 0.001x2 Reorder the terms: 525 + -1.45x + 0.001x2 = -525 + 525 + 2.45x + -2.45x + -0.001x2 + 0.001x2 Combine like terms: -525 + 525 = 0 525 + -1.45x + 0.001x2 = 0 + 2.45x + -2.45x + -0.001x2 + 0.001x2 525 + -1.45x + 0.001x2 = 2.45x + -2.45x + -0.001x2 + 0.001x2 Combine like terms: 2.45x + -2.45x = 0.00 525 + -1.45x + 0.001x2 = 0.00 + -0.001x2 + 0.001x2 525 + -1.45x + 0.001x2 = -0.001x2 + 0.001x2 Combine like terms: -0.001x2 + 0.001x2 = 0.000 525 + -1.45x + 0.001x2 = 0.000 Begin completing the square. Divide all terms by 0.001 the coefficient of the squared term: Divide each side by '0.001'. 525000 + -1450x + x2 = 0 Move the constant term to the right: Add '-525000' to each side of the equation. 525000 + -1450x + -525000 + x2 = 0 + -525000 Reorder the terms: 525000 + -525000 + -1450x + x2 = 0 + -525000 Combine like terms: 525000 + -525000 = 0 0 + -1450x + x2 = 0 + -525000 -1450x + x2 = 0 + -525000 Combine like terms: 0 + -525000 = -525000 -1450x + x2 = -525000 The x term is -1450x. Take half its coefficient (-725). Square it (525625) and add it to both sides. Add '525625' to each side of the equation. -1450x + 525625 + x2 = -525000 + 525625 Reorder the terms: 525625 + -1450x + x2 = -525000 + 525625 Combine like terms: -525000 + 525625 = 625 525625 + -1450x + x2 = 625 Factor a perfect square on the left side: (x + -725)(x + -725) = 625 Calculate the square root of the right side: 25 Break this problem into two subproblems by setting (x + -725) equal to 25 and -25.Subproblem 1
x + -725 = 25 Simplifying x + -725 = 25 Reorder the terms: -725 + x = 25 Solving -725 + x = 25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '725' to each side of the equation. -725 + 725 + x = 25 + 725 Combine like terms: -725 + 725 = 0 0 + x = 25 + 725 x = 25 + 725 Combine like terms: 25 + 725 = 750 x = 750 Simplifying x = 750Subproblem 2
x + -725 = -25 Simplifying x + -725 = -25 Reorder the terms: -725 + x = -25 Solving -725 + x = -25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '725' to each side of the equation. -725 + 725 + x = -25 + 725 Combine like terms: -725 + 725 = 0 0 + x = -25 + 725 x = -25 + 725 Combine like terms: -25 + 725 = 700 x = 700 Simplifying x = 700Solution
The solution to the problem is based on the solutions from the subproblems. x = {750, 700}
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