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Simplifying x2 + x + -8 = 391 Reorder the terms: -8 + x + x2 = 391 Solving -8 + x + x2 = 391 Solving for variable 'x'. Reorder the terms: -8 + -391 + x + x2 = 391 + -391 Combine like terms: -8 + -391 = -399 -399 + x + x2 = 391 + -391 Combine like terms: 391 + -391 = 0 -399 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '399' to each side of the equation. -399 + x + 399 + x2 = 0 + 399 Reorder the terms: -399 + 399 + x + x2 = 0 + 399 Combine like terms: -399 + 399 = 0 0 + x + x2 = 0 + 399 x + x2 = 0 + 399 Combine like terms: 0 + 399 = 399 x + x2 = 399 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 = 399 + 0.25 Reorder the terms: 0.25 + x + x2 = 399 + 0.25 Combine like terms: 399 + 0.25 = 399.25 0.25 + x + x2 = 399.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 399.25 Calculate the square root of the right side: 19.981241203 Break this problem into two subproblems by setting (x + 0.5) equal to 19.981241203 and -19.981241203.Subproblem 1
x + 0.5 = 19.981241203 Simplifying x + 0.5 = 19.981241203 Reorder the terms: 0.5 + x = 19.981241203 Solving 0.5 + x = 19.981241203 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 = 19.981241203 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 19.981241203 + -0.5 x = 19.981241203 + -0.5 Combine like terms: 19.981241203 + -0.5 = 19.481241203 x = 19.481241203 Simplifying x = 19.481241203Subproblem 2
x + 0.5 = -19.981241203 Simplifying x + 0.5 = -19.981241203 Reorder the terms: 0.5 + x = -19.981241203 Solving 0.5 + x = -19.981241203 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 = -19.981241203 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -19.981241203 + -0.5 x = -19.981241203 + -0.5 Combine like terms: -19.981241203 + -0.5 = -20.481241203 x = -20.481241203 Simplifying x = -20.481241203Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.481241203, -20.481241203}
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