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Simplifying x2 + 2x + -6.1 = 0 Reorder the terms: -6.1 + 2x + x2 = 0 Solving -6.1 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '6.1' to each side of the equation. -6.1 + 2x + 6.1 + x2 = 0 + 6.1 Reorder the terms: -6.1 + 6.1 + 2x + x2 = 0 + 6.1 Combine like terms: -6.1 + 6.1 = 0.0 0.0 + 2x + x2 = 0 + 6.1 2x + x2 = 0 + 6.1 Combine like terms: 0 + 6.1 = 6.1 2x + x2 = 6.1 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 = 6.1 + 1 Reorder the terms: 1 + 2x + x2 = 6.1 + 1 Combine like terms: 6.1 + 1 = 7.1 1 + 2x + x2 = 7.1 Factor a perfect square on the left side: (x + 1)(x + 1) = 7.1 Calculate the square root of the right side: 2.664582519 Break this problem into two subproblems by setting (x + 1) equal to 2.664582519 and -2.664582519.Subproblem 1
x + 1 = 2.664582519 Simplifying x + 1 = 2.664582519 Reorder the terms: 1 + x = 2.664582519 Solving 1 + x = 2.664582519 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 = 2.664582519 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.664582519 + -1 x = 2.664582519 + -1 Combine like terms: 2.664582519 + -1 = 1.664582519 x = 1.664582519 Simplifying x = 1.664582519Subproblem 2
x + 1 = -2.664582519 Simplifying x + 1 = -2.664582519 Reorder the terms: 1 + x = -2.664582519 Solving 1 + x = -2.664582519 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 = -2.664582519 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.664582519 + -1 x = -2.664582519 + -1 Combine like terms: -2.664582519 + -1 = -3.664582519 x = -3.664582519 Simplifying x = -3.664582519Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.664582519, -3.664582519}
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