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Simplifying x(x + 2) = 83 Reorder the terms: x(2 + x) = 83 (2 * x + x * x) = 83 (2x + x2) = 83 Solving 2x + x2 = 83 Solving for variable 'x'. Reorder the terms: -83 + 2x + x2 = 83 + -83 Combine like terms: 83 + -83 = 0 -83 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '83' to each side of the equation. -83 + 2x + 83 + x2 = 0 + 83 Reorder the terms: -83 + 83 + 2x + x2 = 0 + 83 Combine like terms: -83 + 83 = 0 0 + 2x + x2 = 0 + 83 2x + x2 = 0 + 83 Combine like terms: 0 + 83 = 83 2x + x2 = 83 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 = 83 + 1 Reorder the terms: 1 + 2x + x2 = 83 + 1 Combine like terms: 83 + 1 = 84 1 + 2x + x2 = 84 Factor a perfect square on the left side: (x + 1)(x + 1) = 84 Calculate the square root of the right side: 9.16515139 Break this problem into two subproblems by setting (x + 1) equal to 9.16515139 and -9.16515139.Subproblem 1
x + 1 = 9.16515139 Simplifying x + 1 = 9.16515139 Reorder the terms: 1 + x = 9.16515139 Solving 1 + x = 9.16515139 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 = 9.16515139 + -1 Combine like terms: 1 + -1 = 0 0 + x = 9.16515139 + -1 x = 9.16515139 + -1 Combine like terms: 9.16515139 + -1 = 8.16515139 x = 8.16515139 Simplifying x = 8.16515139Subproblem 2
x + 1 = -9.16515139 Simplifying x + 1 = -9.16515139 Reorder the terms: 1 + x = -9.16515139 Solving 1 + x = -9.16515139 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 = -9.16515139 + -1 Combine like terms: 1 + -1 = 0 0 + x = -9.16515139 + -1 x = -9.16515139 + -1 Combine like terms: -9.16515139 + -1 = -10.16515139 x = -10.16515139 Simplifying x = -10.16515139Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.16515139, -10.16515139}
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