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Simplifying x(x + 28) + 3(x + -34) = 939 Reorder the terms: x(28 + x) + 3(x + -34) = 939 (28 * x + x * x) + 3(x + -34) = 939 (28x + x2) + 3(x + -34) = 939 Reorder the terms: 28x + x2 + 3(-34 + x) = 939 28x + x2 + (-34 * 3 + x * 3) = 939 28x + x2 + (-102 + 3x) = 939 Reorder the terms: -102 + 28x + 3x + x2 = 939 Combine like terms: 28x + 3x = 31x -102 + 31x + x2 = 939 Solving -102 + 31x + x2 = 939 Solving for variable 'x'. Reorder the terms: -102 + -939 + 31x + x2 = 939 + -939 Combine like terms: -102 + -939 = -1041 -1041 + 31x + x2 = 939 + -939 Combine like terms: 939 + -939 = 0 -1041 + 31x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1041' to each side of the equation. -1041 + 31x + 1041 + x2 = 0 + 1041 Reorder the terms: -1041 + 1041 + 31x + x2 = 0 + 1041 Combine like terms: -1041 + 1041 = 0 0 + 31x + x2 = 0 + 1041 31x + x2 = 0 + 1041 Combine like terms: 0 + 1041 = 1041 31x + x2 = 1041 The x term is 31x. Take half its coefficient (15.5). Square it (240.25) and add it to both sides. Add '240.25' to each side of the equation. 31x + 240.25 + x2 = 1041 + 240.25 Reorder the terms: 240.25 + 31x + x2 = 1041 + 240.25 Combine like terms: 1041 + 240.25 = 1281.25 240.25 + 31x + x2 = 1281.25 Factor a perfect square on the left side: (x + 15.5)(x + 15.5) = 1281.25 Calculate the square root of the right side: 35.794552658 Break this problem into two subproblems by setting (x + 15.5) equal to 35.794552658 and -35.794552658.Subproblem 1
x + 15.5 = 35.794552658 Simplifying x + 15.5 = 35.794552658 Reorder the terms: 15.5 + x = 35.794552658 Solving 15.5 + x = 35.794552658 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15.5' to each side of the equation. 15.5 + -15.5 + x = 35.794552658 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + x = 35.794552658 + -15.5 x = 35.794552658 + -15.5 Combine like terms: 35.794552658 + -15.5 = 20.294552658 x = 20.294552658 Simplifying x = 20.294552658Subproblem 2
x + 15.5 = -35.794552658 Simplifying x + 15.5 = -35.794552658 Reorder the terms: 15.5 + x = -35.794552658 Solving 15.5 + x = -35.794552658 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15.5' to each side of the equation. 15.5 + -15.5 + x = -35.794552658 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + x = -35.794552658 + -15.5 x = -35.794552658 + -15.5 Combine like terms: -35.794552658 + -15.5 = -51.294552658 x = -51.294552658 Simplifying x = -51.294552658Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.294552658, -51.294552658}
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