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Simplifying x2 + -2x + -81 = 0 Reorder the terms: -81 + -2x + x2 = 0 Solving -81 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '81' to each side of the equation. -81 + -2x + 81 + x2 = 0 + 81 Reorder the terms: -81 + 81 + -2x + x2 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + -2x + x2 = 0 + 81 -2x + x2 = 0 + 81 Combine like terms: 0 + 81 = 81 -2x + x2 = 81 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 = 81 + 1 Reorder the terms: 1 + -2x + x2 = 81 + 1 Combine like terms: 81 + 1 = 82 1 + -2x + x2 = 82 Factor a perfect square on the left side: (x + -1)(x + -1) = 82 Calculate the square root of the right side: 9.055385138 Break this problem into two subproblems by setting (x + -1) equal to 9.055385138 and -9.055385138.Subproblem 1
x + -1 = 9.055385138 Simplifying x + -1 = 9.055385138 Reorder the terms: -1 + x = 9.055385138 Solving -1 + x = 9.055385138 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 = 9.055385138 + 1 Combine like terms: -1 + 1 = 0 0 + x = 9.055385138 + 1 x = 9.055385138 + 1 Combine like terms: 9.055385138 + 1 = 10.055385138 x = 10.055385138 Simplifying x = 10.055385138Subproblem 2
x + -1 = -9.055385138 Simplifying x + -1 = -9.055385138 Reorder the terms: -1 + x = -9.055385138 Solving -1 + x = -9.055385138 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 = -9.055385138 + 1 Combine like terms: -1 + 1 = 0 0 + x = -9.055385138 + 1 x = -9.055385138 + 1 Combine like terms: -9.055385138 + 1 = -8.055385138 x = -8.055385138 Simplifying x = -8.055385138Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.055385138, -8.055385138}
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