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Simplifying x2 + -6x + -31 = 0 Reorder the terms: -31 + -6x + x2 = 0 Solving -31 + -6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '31' to each side of the equation. -31 + -6x + 31 + x2 = 0 + 31 Reorder the terms: -31 + 31 + -6x + x2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + -6x + x2 = 0 + 31 -6x + x2 = 0 + 31 Combine like terms: 0 + 31 = 31 -6x + x2 = 31 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 31 + 9 Reorder the terms: 9 + -6x + x2 = 31 + 9 Combine like terms: 31 + 9 = 40 9 + -6x + x2 = 40 Factor a perfect square on the left side: (x + -3)(x + -3) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (x + -3) equal to 6.32455532 and -6.32455532.Subproblem 1
x + -3 = 6.32455532 Simplifying x + -3 = 6.32455532 Reorder the terms: -3 + x = 6.32455532 Solving -3 + x = 6.32455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 6.32455532 + 3 Combine like terms: -3 + 3 = 0 0 + x = 6.32455532 + 3 x = 6.32455532 + 3 Combine like terms: 6.32455532 + 3 = 9.32455532 x = 9.32455532 Simplifying x = 9.32455532Subproblem 2
x + -3 = -6.32455532 Simplifying x + -3 = -6.32455532 Reorder the terms: -3 + x = -6.32455532 Solving -3 + x = -6.32455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -6.32455532 + 3 Combine like terms: -3 + 3 = 0 0 + x = -6.32455532 + 3 x = -6.32455532 + 3 Combine like terms: -6.32455532 + 3 = -3.32455532 x = -3.32455532 Simplifying x = -3.32455532Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.32455532, -3.32455532}
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