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Simplifying x2 + 2x + -462 = 0 Reorder the terms: -462 + 2x + x2 = 0 Solving -462 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '462' to each side of the equation. -462 + 2x + 462 + x2 = 0 + 462 Reorder the terms: -462 + 462 + 2x + x2 = 0 + 462 Combine like terms: -462 + 462 = 0 0 + 2x + x2 = 0 + 462 2x + x2 = 0 + 462 Combine like terms: 0 + 462 = 462 2x + x2 = 462 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 = 462 + 1 Reorder the terms: 1 + 2x + x2 = 462 + 1 Combine like terms: 462 + 1 = 463 1 + 2x + x2 = 463 Factor a perfect square on the left side: (x + 1)(x + 1) = 463 Calculate the square root of the right side: 21.517434791 Break this problem into two subproblems by setting (x + 1) equal to 21.517434791 and -21.517434791.Subproblem 1
x + 1 = 21.517434791 Simplifying x + 1 = 21.517434791 Reorder the terms: 1 + x = 21.517434791 Solving 1 + x = 21.517434791 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 = 21.517434791 + -1 Combine like terms: 1 + -1 = 0 0 + x = 21.517434791 + -1 x = 21.517434791 + -1 Combine like terms: 21.517434791 + -1 = 20.517434791 x = 20.517434791 Simplifying x = 20.517434791Subproblem 2
x + 1 = -21.517434791 Simplifying x + 1 = -21.517434791 Reorder the terms: 1 + x = -21.517434791 Solving 1 + x = -21.517434791 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 = -21.517434791 + -1 Combine like terms: 1 + -1 = 0 0 + x = -21.517434791 + -1 x = -21.517434791 + -1 Combine like terms: -21.517434791 + -1 = -22.517434791 x = -22.517434791 Simplifying x = -22.517434791Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.517434791, -22.517434791}
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