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Simplifying X(X + 134) = 2700 Reorder the terms: X(134 + X) = 2700 (134 * X + X * X) = 2700 (134X + X2) = 2700 Solving 134X + X2 = 2700 Solving for variable 'X'. Reorder the terms: -2700 + 134X + X2 = 2700 + -2700 Combine like terms: 2700 + -2700 = 0 -2700 + 134X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '2700' to each side of the equation. -2700 + 134X + 2700 + X2 = 0 + 2700 Reorder the terms: -2700 + 2700 + 134X + X2 = 0 + 2700 Combine like terms: -2700 + 2700 = 0 0 + 134X + X2 = 0 + 2700 134X + X2 = 0 + 2700 Combine like terms: 0 + 2700 = 2700 134X + X2 = 2700 The X term is 134X. Take half its coefficient (67). Square it (4489) and add it to both sides. Add '4489' to each side of the equation. 134X + 4489 + X2 = 2700 + 4489 Reorder the terms: 4489 + 134X + X2 = 2700 + 4489 Combine like terms: 2700 + 4489 = 7189 4489 + 134X + X2 = 7189 Factor a perfect square on the left side: (X + 67)(X + 67) = 7189 Calculate the square root of the right side: 84.787970845 Break this problem into two subproblems by setting (X + 67) equal to 84.787970845 and -84.787970845.Subproblem 1
X + 67 = 84.787970845 Simplifying X + 67 = 84.787970845 Reorder the terms: 67 + X = 84.787970845 Solving 67 + X = 84.787970845 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-67' to each side of the equation. 67 + -67 + X = 84.787970845 + -67 Combine like terms: 67 + -67 = 0 0 + X = 84.787970845 + -67 X = 84.787970845 + -67 Combine like terms: 84.787970845 + -67 = 17.787970845 X = 17.787970845 Simplifying X = 17.787970845Subproblem 2
X + 67 = -84.787970845 Simplifying X + 67 = -84.787970845 Reorder the terms: 67 + X = -84.787970845 Solving 67 + X = -84.787970845 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-67' to each side of the equation. 67 + -67 + X = -84.787970845 + -67 Combine like terms: 67 + -67 = 0 0 + X = -84.787970845 + -67 X = -84.787970845 + -67 Combine like terms: -84.787970845 + -67 = -151.787970845 X = -151.787970845 Simplifying X = -151.787970845Solution
The solution to the problem is based on the solutions from the subproblems. X = {17.787970845, -151.787970845}
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