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Simplifying 0 = x2 + 2x + -81 Reorder the terms: 0 = -81 + 2x + x2 Solving 0 = -81 + 2x + x2 Solving for variable 'x'. Combine like terms: 0 + 81 = 81 81 + -2x + -1x2 = -81 + 2x + x2 + 81 + -2x + -1x2 Reorder the terms: 81 + -2x + -1x2 = -81 + 81 + 2x + -2x + x2 + -1x2 Combine like terms: -81 + 81 = 0 81 + -2x + -1x2 = 0 + 2x + -2x + x2 + -1x2 81 + -2x + -1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 81 + -2x + -1x2 = 0 + x2 + -1x2 81 + -2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 81 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -81 + 2x + x2 = 0 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 = 8.055385138 x = 8.055385138 Simplifying x = 8.055385138Subproblem 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 = -10.055385138 x = -10.055385138 Simplifying x = -10.055385138Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.055385138, -10.055385138}
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