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Simplifying x2 + 2x + -272 = 0 Reorder the terms: -272 + 2x + x2 = 0 Solving -272 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '272' to each side of the equation. -272 + 2x + 272 + x2 = 0 + 272 Reorder the terms: -272 + 272 + 2x + x2 = 0 + 272 Combine like terms: -272 + 272 = 0 0 + 2x + x2 = 0 + 272 2x + x2 = 0 + 272 Combine like terms: 0 + 272 = 272 2x + x2 = 272 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 = 272 + 1 Reorder the terms: 1 + 2x + x2 = 272 + 1 Combine like terms: 272 + 1 = 273 1 + 2x + x2 = 273 Factor a perfect square on the left side: (x + 1)(x + 1) = 273 Calculate the square root of the right side: 16.522711642 Break this problem into two subproblems by setting (x + 1) equal to 16.522711642 and -16.522711642.Subproblem 1
x + 1 = 16.522711642 Simplifying x + 1 = 16.522711642 Reorder the terms: 1 + x = 16.522711642 Solving 1 + x = 16.522711642 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 = 16.522711642 + -1 Combine like terms: 1 + -1 = 0 0 + x = 16.522711642 + -1 x = 16.522711642 + -1 Combine like terms: 16.522711642 + -1 = 15.522711642 x = 15.522711642 Simplifying x = 15.522711642Subproblem 2
x + 1 = -16.522711642 Simplifying x + 1 = -16.522711642 Reorder the terms: 1 + x = -16.522711642 Solving 1 + x = -16.522711642 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 = -16.522711642 + -1 Combine like terms: 1 + -1 = 0 0 + x = -16.522711642 + -1 x = -16.522711642 + -1 Combine like terms: -16.522711642 + -1 = -17.522711642 x = -17.522711642 Simplifying x = -17.522711642Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.522711642, -17.522711642}
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