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Simplifying x2 + x + 7 = 392 Reorder the terms: 7 + x + x2 = 392 Solving 7 + x + x2 = 392 Solving for variable 'x'. Reorder the terms: 7 + -392 + x + x2 = 392 + -392 Combine like terms: 7 + -392 = -385 -385 + x + x2 = 392 + -392 Combine like terms: 392 + -392 = 0 -385 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '385' to each side of the equation. -385 + x + 385 + x2 = 0 + 385 Reorder the terms: -385 + 385 + x + x2 = 0 + 385 Combine like terms: -385 + 385 = 0 0 + x + x2 = 0 + 385 x + x2 = 0 + 385 Combine like terms: 0 + 385 = 385 x + x2 = 385 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 385 + 0.25 Reorder the terms: 0.25 + x + x2 = 385 + 0.25 Combine like terms: 385 + 0.25 = 385.25 0.25 + x + x2 = 385.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 385.25 Calculate the square root of the right side: 19.627786426 Break this problem into two subproblems by setting (x + 0.5) equal to 19.627786426 and -19.627786426.Subproblem 1
x + 0.5 = 19.627786426 Simplifying x + 0.5 = 19.627786426 Reorder the terms: 0.5 + x = 19.627786426 Solving 0.5 + x = 19.627786426 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 19.627786426 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 19.627786426 + -0.5 x = 19.627786426 + -0.5 Combine like terms: 19.627786426 + -0.5 = 19.127786426 x = 19.127786426 Simplifying x = 19.127786426Subproblem 2
x + 0.5 = -19.627786426 Simplifying x + 0.5 = -19.627786426 Reorder the terms: 0.5 + x = -19.627786426 Solving 0.5 + x = -19.627786426 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -19.627786426 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -19.627786426 + -0.5 x = -19.627786426 + -0.5 Combine like terms: -19.627786426 + -0.5 = -20.127786426 x = -20.127786426 Simplifying x = -20.127786426Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.127786426, -20.127786426}
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