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Simplifying -125x + 3000 = 60 + x * x Reorder the terms: 3000 + -125x = 60 + x * x Multiply x * x 3000 + -125x = 60 + x2 Solving 3000 + -125x = 60 + x2 Solving for variable 'x'. Reorder the terms: 3000 + -60 + -125x + -1x2 = 60 + x2 + -60 + -1x2 Combine like terms: 3000 + -60 = 2940 2940 + -125x + -1x2 = 60 + x2 + -60 + -1x2 Reorder the terms: 2940 + -125x + -1x2 = 60 + -60 + x2 + -1x2 Combine like terms: 60 + -60 = 0 2940 + -125x + -1x2 = 0 + x2 + -1x2 2940 + -125x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 2940 + -125x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2940 + 125x + x2 = 0 Move the constant term to the right: Add '2940' to each side of the equation. -2940 + 125x + 2940 + x2 = 0 + 2940 Reorder the terms: -2940 + 2940 + 125x + x2 = 0 + 2940 Combine like terms: -2940 + 2940 = 0 0 + 125x + x2 = 0 + 2940 125x + x2 = 0 + 2940 Combine like terms: 0 + 2940 = 2940 125x + x2 = 2940 The x term is 125x. Take half its coefficient (62.5). Square it (3906.25) and add it to both sides. Add '3906.25' to each side of the equation. 125x + 3906.25 + x2 = 2940 + 3906.25 Reorder the terms: 3906.25 + 125x + x2 = 2940 + 3906.25 Combine like terms: 2940 + 3906.25 = 6846.25 3906.25 + 125x + x2 = 6846.25 Factor a perfect square on the left side: (x + 62.5)(x + 62.5) = 6846.25 Calculate the square root of the right side: 82.742069106 Break this problem into two subproblems by setting (x + 62.5) equal to 82.742069106 and -82.742069106.Subproblem 1
x + 62.5 = 82.742069106 Simplifying x + 62.5 = 82.742069106 Reorder the terms: 62.5 + x = 82.742069106 Solving 62.5 + x = 82.742069106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-62.5' to each side of the equation. 62.5 + -62.5 + x = 82.742069106 + -62.5 Combine like terms: 62.5 + -62.5 = 0.0 0.0 + x = 82.742069106 + -62.5 x = 82.742069106 + -62.5 Combine like terms: 82.742069106 + -62.5 = 20.242069106 x = 20.242069106 Simplifying x = 20.242069106Subproblem 2
x + 62.5 = -82.742069106 Simplifying x + 62.5 = -82.742069106 Reorder the terms: 62.5 + x = -82.742069106 Solving 62.5 + x = -82.742069106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-62.5' to each side of the equation. 62.5 + -62.5 + x = -82.742069106 + -62.5 Combine like terms: 62.5 + -62.5 = 0.0 0.0 + x = -82.742069106 + -62.5 x = -82.742069106 + -62.5 Combine like terms: -82.742069106 + -62.5 = -145.242069106 x = -145.242069106 Simplifying x = -145.242069106Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.242069106, -145.242069106}
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