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Simplifying 3x2 + -18x + -31 = 0 Reorder the terms: -31 + -18x + 3x2 = 0 Solving -31 + -18x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -10.33333333 + -6x + x2 = 0 Move the constant term to the right: Add '10.33333333' to each side of the equation. -10.33333333 + -6x + 10.33333333 + x2 = 0 + 10.33333333 Reorder the terms: -10.33333333 + 10.33333333 + -6x + x2 = 0 + 10.33333333 Combine like terms: -10.33333333 + 10.33333333 = 0.00000000 0.00000000 + -6x + x2 = 0 + 10.33333333 -6x + x2 = 0 + 10.33333333 Combine like terms: 0 + 10.33333333 = 10.33333333 -6x + x2 = 10.33333333 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 = 10.33333333 + 9 Reorder the terms: 9 + -6x + x2 = 10.33333333 + 9 Combine like terms: 10.33333333 + 9 = 19.33333333 9 + -6x + x2 = 19.33333333 Factor a perfect square on the left side: (x + -3)(x + -3) = 19.33333333 Calculate the square root of the right side: 4.396968652 Break this problem into two subproblems by setting (x + -3) equal to 4.396968652 and -4.396968652.Subproblem 1
x + -3 = 4.396968652 Simplifying x + -3 = 4.396968652 Reorder the terms: -3 + x = 4.396968652 Solving -3 + x = 4.396968652 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 = 4.396968652 + 3 Combine like terms: -3 + 3 = 0 0 + x = 4.396968652 + 3 x = 4.396968652 + 3 Combine like terms: 4.396968652 + 3 = 7.396968652 x = 7.396968652 Simplifying x = 7.396968652Subproblem 2
x + -3 = -4.396968652 Simplifying x + -3 = -4.396968652 Reorder the terms: -3 + x = -4.396968652 Solving -3 + x = -4.396968652 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 = -4.396968652 + 3 Combine like terms: -3 + 3 = 0 0 + x = -4.396968652 + 3 x = -4.396968652 + 3 Combine like terms: -4.396968652 + 3 = -1.396968652 x = -1.396968652 Simplifying x = -1.396968652Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.396968652, -1.396968652}
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