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Simplifying x2 + -100x + 2400 = 325 Reorder the terms: 2400 + -100x + x2 = 325 Solving 2400 + -100x + x2 = 325 Solving for variable 'x'. Reorder the terms: 2400 + -325 + -100x + x2 = 325 + -325 Combine like terms: 2400 + -325 = 2075 2075 + -100x + x2 = 325 + -325 Combine like terms: 325 + -325 = 0 2075 + -100x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2075' to each side of the equation. 2075 + -100x + -2075 + x2 = 0 + -2075 Reorder the terms: 2075 + -2075 + -100x + x2 = 0 + -2075 Combine like terms: 2075 + -2075 = 0 0 + -100x + x2 = 0 + -2075 -100x + x2 = 0 + -2075 Combine like terms: 0 + -2075 = -2075 -100x + x2 = -2075 The x term is -100x. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100x + 2500 + x2 = -2075 + 2500 Reorder the terms: 2500 + -100x + x2 = -2075 + 2500 Combine like terms: -2075 + 2500 = 425 2500 + -100x + x2 = 425 Factor a perfect square on the left side: (x + -50)(x + -50) = 425 Calculate the square root of the right side: 20.615528128 Break this problem into two subproblems by setting (x + -50) equal to 20.615528128 and -20.615528128.Subproblem 1
x + -50 = 20.615528128 Simplifying x + -50 = 20.615528128 Reorder the terms: -50 + x = 20.615528128 Solving -50 + x = 20.615528128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 20.615528128 + 50 Combine like terms: -50 + 50 = 0 0 + x = 20.615528128 + 50 x = 20.615528128 + 50 Combine like terms: 20.615528128 + 50 = 70.615528128 x = 70.615528128 Simplifying x = 70.615528128Subproblem 2
x + -50 = -20.615528128 Simplifying x + -50 = -20.615528128 Reorder the terms: -50 + x = -20.615528128 Solving -50 + x = -20.615528128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -20.615528128 + 50 Combine like terms: -50 + 50 = 0 0 + x = -20.615528128 + 50 x = -20.615528128 + 50 Combine like terms: -20.615528128 + 50 = 29.384471872 x = 29.384471872 Simplifying x = 29.384471872Solution
The solution to the problem is based on the solutions from the subproblems. x = {70.615528128, 29.384471872}
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