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Simplifying x2 + x + -280 = 0 Reorder the terms: -280 + x + x2 = 0 Solving -280 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '280' to each side of the equation. -280 + x + 280 + x2 = 0 + 280 Reorder the terms: -280 + 280 + x + x2 = 0 + 280 Combine like terms: -280 + 280 = 0 0 + x + x2 = 0 + 280 x + x2 = 0 + 280 Combine like terms: 0 + 280 = 280 x + x2 = 280 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 = 280 + 0.25 Reorder the terms: 0.25 + x + x2 = 280 + 0.25 Combine like terms: 280 + 0.25 = 280.25 0.25 + x + x2 = 280.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 280.25 Calculate the square root of the right side: 16.740669043 Break this problem into two subproblems by setting (x + 0.5) equal to 16.740669043 and -16.740669043.Subproblem 1
x + 0.5 = 16.740669043 Simplifying x + 0.5 = 16.740669043 Reorder the terms: 0.5 + x = 16.740669043 Solving 0.5 + x = 16.740669043 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 = 16.740669043 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 16.740669043 + -0.5 x = 16.740669043 + -0.5 Combine like terms: 16.740669043 + -0.5 = 16.240669043 x = 16.240669043 Simplifying x = 16.240669043Subproblem 2
x + 0.5 = -16.740669043 Simplifying x + 0.5 = -16.740669043 Reorder the terms: 0.5 + x = -16.740669043 Solving 0.5 + x = -16.740669043 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 = -16.740669043 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -16.740669043 + -0.5 x = -16.740669043 + -0.5 Combine like terms: -16.740669043 + -0.5 = -17.240669043 x = -17.240669043 Simplifying x = -17.240669043Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.240669043, -17.240669043}
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