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Simplifying X2 + 15X = 9950 Reorder the terms: 15X + X2 = 9950 Solving 15X + X2 = 9950 Solving for variable 'X'. Reorder the terms: -9950 + 15X + X2 = 9950 + -9950 Combine like terms: 9950 + -9950 = 0 -9950 + 15X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '9950' to each side of the equation. -9950 + 15X + 9950 + X2 = 0 + 9950 Reorder the terms: -9950 + 9950 + 15X + X2 = 0 + 9950 Combine like terms: -9950 + 9950 = 0 0 + 15X + X2 = 0 + 9950 15X + X2 = 0 + 9950 Combine like terms: 0 + 9950 = 9950 15X + X2 = 9950 The X term is 15X. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15X + 56.25 + X2 = 9950 + 56.25 Reorder the terms: 56.25 + 15X + X2 = 9950 + 56.25 Combine like terms: 9950 + 56.25 = 10006.25 56.25 + 15X + X2 = 10006.25 Factor a perfect square on the left side: (X + 7.5)(X + 7.5) = 10006.25 Calculate the square root of the right side: 100.031245119 Break this problem into two subproblems by setting (X + 7.5) equal to 100.031245119 and -100.031245119.Subproblem 1
X + 7.5 = 100.031245119 Simplifying X + 7.5 = 100.031245119 Reorder the terms: 7.5 + X = 100.031245119 Solving 7.5 + X = 100.031245119 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + X = 100.031245119 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + X = 100.031245119 + -7.5 X = 100.031245119 + -7.5 Combine like terms: 100.031245119 + -7.5 = 92.531245119 X = 92.531245119 Simplifying X = 92.531245119Subproblem 2
X + 7.5 = -100.031245119 Simplifying X + 7.5 = -100.031245119 Reorder the terms: 7.5 + X = -100.031245119 Solving 7.5 + X = -100.031245119 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + X = -100.031245119 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + X = -100.031245119 + -7.5 X = -100.031245119 + -7.5 Combine like terms: -100.031245119 + -7.5 = -107.531245119 X = -107.531245119 Simplifying X = -107.531245119Solution
The solution to the problem is based on the solutions from the subproblems. X = {92.531245119, -107.531245119}
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