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Simplifying 0 = 6x + x2 + -31 Reorder the terms: 0 = -31 + 6x + x2 Solving 0 = -31 + 6x + x2 Solving for variable 'x'. Combine like terms: 0 + 31 = 31 31 + -6x + -1x2 = -31 + 6x + x2 + 31 + -6x + -1x2 Reorder the terms: 31 + -6x + -1x2 = -31 + 31 + 6x + -6x + x2 + -1x2 Combine like terms: -31 + 31 = 0 31 + -6x + -1x2 = 0 + 6x + -6x + x2 + -1x2 31 + -6x + -1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 31 + -6x + -1x2 = 0 + x2 + -1x2 31 + -6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 31 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -31 + 6x + x2 = 0 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 = 3.32455532 x = 3.32455532 Simplifying x = 3.32455532Subproblem 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 = -9.32455532 x = -9.32455532 Simplifying x = -9.32455532Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.32455532, -9.32455532}
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