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Simplifying x2 + 2x = 6460 Reorder the terms: 2x + x2 = 6460 Solving 2x + x2 = 6460 Solving for variable 'x'. Reorder the terms: -6460 + 2x + x2 = 6460 + -6460 Combine like terms: 6460 + -6460 = 0 -6460 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '6460' to each side of the equation. -6460 + 2x + 6460 + x2 = 0 + 6460 Reorder the terms: -6460 + 6460 + 2x + x2 = 0 + 6460 Combine like terms: -6460 + 6460 = 0 0 + 2x + x2 = 0 + 6460 2x + x2 = 0 + 6460 Combine like terms: 0 + 6460 = 6460 2x + x2 = 6460 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 6460 + 1 Reorder the terms: 1 + 2x + x2 = 6460 + 1 Combine like terms: 6460 + 1 = 6461 1 + 2x + x2 = 6461 Factor a perfect square on the left side: (x + 1)(x + 1) = 6461 Calculate the square root of the right side: 80.380345856 Break this problem into two subproblems by setting (x + 1) equal to 80.380345856 and -80.380345856.Subproblem 1
x + 1 = 80.380345856 Simplifying x + 1 = 80.380345856 Reorder the terms: 1 + x = 80.380345856 Solving 1 + x = 80.380345856 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 80.380345856 + -1 Combine like terms: 1 + -1 = 0 0 + x = 80.380345856 + -1 x = 80.380345856 + -1 Combine like terms: 80.380345856 + -1 = 79.380345856 x = 79.380345856 Simplifying x = 79.380345856Subproblem 2
x + 1 = -80.380345856 Simplifying x + 1 = -80.380345856 Reorder the terms: 1 + x = -80.380345856 Solving 1 + x = -80.380345856 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -80.380345856 + -1 Combine like terms: 1 + -1 = 0 0 + x = -80.380345856 + -1 x = -80.380345856 + -1 Combine like terms: -80.380345856 + -1 = -81.380345856 x = -81.380345856 Simplifying x = -81.380345856Solution
The solution to the problem is based on the solutions from the subproblems. x = {79.380345856, -81.380345856}
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