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Simplifying x2 + -2x + -39 = 0 Reorder the terms: -39 + -2x + x2 = 0 Solving -39 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '39' to each side of the equation. -39 + -2x + 39 + x2 = 0 + 39 Reorder the terms: -39 + 39 + -2x + x2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + -2x + x2 = 0 + 39 -2x + x2 = 0 + 39 Combine like terms: 0 + 39 = 39 -2x + x2 = 39 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 = 39 + 1 Reorder the terms: 1 + -2x + x2 = 39 + 1 Combine like terms: 39 + 1 = 40 1 + -2x + x2 = 40 Factor a perfect square on the left side: (x + -1)(x + -1) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (x + -1) equal to 6.32455532 and -6.32455532.Subproblem 1
x + -1 = 6.32455532 Simplifying x + -1 = 6.32455532 Reorder the terms: -1 + x = 6.32455532 Solving -1 + x = 6.32455532 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 = 6.32455532 + 1 Combine like terms: -1 + 1 = 0 0 + x = 6.32455532 + 1 x = 6.32455532 + 1 Combine like terms: 6.32455532 + 1 = 7.32455532 x = 7.32455532 Simplifying x = 7.32455532Subproblem 2
x + -1 = -6.32455532 Simplifying x + -1 = -6.32455532 Reorder the terms: -1 + x = -6.32455532 Solving -1 + x = -6.32455532 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 = -6.32455532 + 1 Combine like terms: -1 + 1 = 0 0 + x = -6.32455532 + 1 x = -6.32455532 + 1 Combine like terms: -6.32455532 + 1 = -5.32455532 x = -5.32455532 Simplifying x = -5.32455532Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.32455532, -5.32455532}
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