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Simplifying x2 + 0.21x = 5352 Reorder the terms: 0.21x + x2 = 5352 Solving 0.21x + x2 = 5352 Solving for variable 'x'. Reorder the terms: -5352 + 0.21x + x2 = 5352 + -5352 Combine like terms: 5352 + -5352 = 0 -5352 + 0.21x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5352' to each side of the equation. -5352 + 0.21x + 5352 + x2 = 0 + 5352 Reorder the terms: -5352 + 5352 + 0.21x + x2 = 0 + 5352 Combine like terms: -5352 + 5352 = 0 0 + 0.21x + x2 = 0 + 5352 0.21x + x2 = 0 + 5352 Combine like terms: 0 + 5352 = 5352 0.21x + x2 = 5352 The x term is 0.21x. Take half its coefficient (0.105). Square it (0.011025) and add it to both sides. Add '0.011025' to each side of the equation. 0.21x + 0.011025 + x2 = 5352 + 0.011025 Reorder the terms: 0.011025 + 0.21x + x2 = 5352 + 0.011025 Combine like terms: 5352 + 0.011025 = 5352.011025 0.011025 + 0.21x + x2 = 5352.011025 Factor a perfect square on the left side: (x + 0.105)(x + 0.105) = 5352.011025 Calculate the square root of the right side: 73.157439984 Break this problem into two subproblems by setting (x + 0.105) equal to 73.157439984 and -73.157439984.Subproblem 1
x + 0.105 = 73.157439984 Simplifying x + 0.105 = 73.157439984 Reorder the terms: 0.105 + x = 73.157439984 Solving 0.105 + x = 73.157439984 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.105' to each side of the equation. 0.105 + -0.105 + x = 73.157439984 + -0.105 Combine like terms: 0.105 + -0.105 = 0.000 0.000 + x = 73.157439984 + -0.105 x = 73.157439984 + -0.105 Combine like terms: 73.157439984 + -0.105 = 73.052439984 x = 73.052439984 Simplifying x = 73.052439984Subproblem 2
x + 0.105 = -73.157439984 Simplifying x + 0.105 = -73.157439984 Reorder the terms: 0.105 + x = -73.157439984 Solving 0.105 + x = -73.157439984 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.105' to each side of the equation. 0.105 + -0.105 + x = -73.157439984 + -0.105 Combine like terms: 0.105 + -0.105 = 0.000 0.000 + x = -73.157439984 + -0.105 x = -73.157439984 + -0.105 Combine like terms: -73.157439984 + -0.105 = -73.262439984 x = -73.262439984 Simplifying x = -73.262439984Solution
The solution to the problem is based on the solutions from the subproblems. x = {73.052439984, -73.262439984}
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