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Simplifying x2 + 2x + -3500 = 0 Reorder the terms: -3500 + 2x + x2 = 0 Solving -3500 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3500' to each side of the equation. -3500 + 2x + 3500 + x2 = 0 + 3500 Reorder the terms: -3500 + 3500 + 2x + x2 = 0 + 3500 Combine like terms: -3500 + 3500 = 0 0 + 2x + x2 = 0 + 3500 2x + x2 = 0 + 3500 Combine like terms: 0 + 3500 = 3500 2x + x2 = 3500 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 = 3500 + 1 Reorder the terms: 1 + 2x + x2 = 3500 + 1 Combine like terms: 3500 + 1 = 3501 1 + 2x + x2 = 3501 Factor a perfect square on the left side: (x + 1)(x + 1) = 3501 Calculate the square root of the right side: 59.16924877 Break this problem into two subproblems by setting (x + 1) equal to 59.16924877 and -59.16924877.Subproblem 1
x + 1 = 59.16924877 Simplifying x + 1 = 59.16924877 Reorder the terms: 1 + x = 59.16924877 Solving 1 + x = 59.16924877 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 = 59.16924877 + -1 Combine like terms: 1 + -1 = 0 0 + x = 59.16924877 + -1 x = 59.16924877 + -1 Combine like terms: 59.16924877 + -1 = 58.16924877 x = 58.16924877 Simplifying x = 58.16924877Subproblem 2
x + 1 = -59.16924877 Simplifying x + 1 = -59.16924877 Reorder the terms: 1 + x = -59.16924877 Solving 1 + x = -59.16924877 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 = -59.16924877 + -1 Combine like terms: 1 + -1 = 0 0 + x = -59.16924877 + -1 x = -59.16924877 + -1 Combine like terms: -59.16924877 + -1 = -60.16924877 x = -60.16924877 Simplifying x = -60.16924877Solution
The solution to the problem is based on the solutions from the subproblems. x = {58.16924877, -60.16924877}
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