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Simplifying x2 + 2x = 5000 Reorder the terms: 2x + x2 = 5000 Solving 2x + x2 = 5000 Solving for variable 'x'. Reorder the terms: -5000 + 2x + x2 = 5000 + -5000 Combine like terms: 5000 + -5000 = 0 -5000 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5000' to each side of the equation. -5000 + 2x + 5000 + x2 = 0 + 5000 Reorder the terms: -5000 + 5000 + 2x + x2 = 0 + 5000 Combine like terms: -5000 + 5000 = 0 0 + 2x + x2 = 0 + 5000 2x + x2 = 0 + 5000 Combine like terms: 0 + 5000 = 5000 2x + x2 = 5000 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 = 5000 + 1 Reorder the terms: 1 + 2x + x2 = 5000 + 1 Combine like terms: 5000 + 1 = 5001 1 + 2x + x2 = 5001 Factor a perfect square on the left side: (x + 1)(x + 1) = 5001 Calculate the square root of the right side: 70.717748833 Break this problem into two subproblems by setting (x + 1) equal to 70.717748833 and -70.717748833.Subproblem 1
x + 1 = 70.717748833 Simplifying x + 1 = 70.717748833 Reorder the terms: 1 + x = 70.717748833 Solving 1 + x = 70.717748833 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 = 70.717748833 + -1 Combine like terms: 1 + -1 = 0 0 + x = 70.717748833 + -1 x = 70.717748833 + -1 Combine like terms: 70.717748833 + -1 = 69.717748833 x = 69.717748833 Simplifying x = 69.717748833Subproblem 2
x + 1 = -70.717748833 Simplifying x + 1 = -70.717748833 Reorder the terms: 1 + x = -70.717748833 Solving 1 + x = -70.717748833 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 = -70.717748833 + -1 Combine like terms: 1 + -1 = 0 0 + x = -70.717748833 + -1 x = -70.717748833 + -1 Combine like terms: -70.717748833 + -1 = -71.717748833 x = -71.717748833 Simplifying x = -71.717748833Solution
The solution to the problem is based on the solutions from the subproblems. x = {69.717748833, -71.717748833}
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