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Simplifying x2 + 2x + 5 = 250 Reorder the terms: 5 + 2x + x2 = 250 Solving 5 + 2x + x2 = 250 Solving for variable 'x'. Reorder the terms: 5 + -250 + 2x + x2 = 250 + -250 Combine like terms: 5 + -250 = -245 -245 + 2x + x2 = 250 + -250 Combine like terms: 250 + -250 = 0 -245 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '245' to each side of the equation. -245 + 2x + 245 + x2 = 0 + 245 Reorder the terms: -245 + 245 + 2x + x2 = 0 + 245 Combine like terms: -245 + 245 = 0 0 + 2x + x2 = 0 + 245 2x + x2 = 0 + 245 Combine like terms: 0 + 245 = 245 2x + x2 = 245 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 = 245 + 1 Reorder the terms: 1 + 2x + x2 = 245 + 1 Combine like terms: 245 + 1 = 246 1 + 2x + x2 = 246 Factor a perfect square on the left side: (x + 1)(x + 1) = 246 Calculate the square root of the right side: 15.684387141 Break this problem into two subproblems by setting (x + 1) equal to 15.684387141 and -15.684387141.Subproblem 1
x + 1 = 15.684387141 Simplifying x + 1 = 15.684387141 Reorder the terms: 1 + x = 15.684387141 Solving 1 + x = 15.684387141 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 = 15.684387141 + -1 Combine like terms: 1 + -1 = 0 0 + x = 15.684387141 + -1 x = 15.684387141 + -1 Combine like terms: 15.684387141 + -1 = 14.684387141 x = 14.684387141 Simplifying x = 14.684387141Subproblem 2
x + 1 = -15.684387141 Simplifying x + 1 = -15.684387141 Reorder the terms: 1 + x = -15.684387141 Solving 1 + x = -15.684387141 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 = -15.684387141 + -1 Combine like terms: 1 + -1 = 0 0 + x = -15.684387141 + -1 x = -15.684387141 + -1 Combine like terms: -15.684387141 + -1 = -16.684387141 x = -16.684387141 Simplifying x = -16.684387141Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.684387141, -16.684387141}
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