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Simplifying 2x + -11 = x2 + -4x + -31 Reorder the terms: -11 + 2x = x2 + -4x + -31 Reorder the terms: -11 + 2x = -31 + -4x + x2 Solving -11 + 2x = -31 + -4x + x2 Solving for variable 'x'. Reorder the terms: -11 + 31 + 2x + 4x + -1x2 = -31 + -4x + x2 + 31 + 4x + -1x2 Combine like terms: -11 + 31 = 20 20 + 2x + 4x + -1x2 = -31 + -4x + x2 + 31 + 4x + -1x2 Combine like terms: 2x + 4x = 6x 20 + 6x + -1x2 = -31 + -4x + x2 + 31 + 4x + -1x2 Reorder the terms: 20 + 6x + -1x2 = -31 + 31 + -4x + 4x + x2 + -1x2 Combine like terms: -31 + 31 = 0 20 + 6x + -1x2 = 0 + -4x + 4x + x2 + -1x2 20 + 6x + -1x2 = -4x + 4x + x2 + -1x2 Combine like terms: -4x + 4x = 0 20 + 6x + -1x2 = 0 + x2 + -1x2 20 + 6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 20 + 6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -20 + -6x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -6x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -6x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -6x + x2 = 0 + 20 -6x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -6x + x2 = 20 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 = 20 + 9 Reorder the terms: 9 + -6x + x2 = 20 + 9 Combine like terms: 20 + 9 = 29 9 + -6x + x2 = 29 Factor a perfect square on the left side: (x + -3)(x + -3) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (x + -3) equal to 5.385164807 and -5.385164807.Subproblem 1
x + -3 = 5.385164807 Simplifying x + -3 = 5.385164807 Reorder the terms: -3 + x = 5.385164807 Solving -3 + x = 5.385164807 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 = 5.385164807 + 3 Combine like terms: -3 + 3 = 0 0 + x = 5.385164807 + 3 x = 5.385164807 + 3 Combine like terms: 5.385164807 + 3 = 8.385164807 x = 8.385164807 Simplifying x = 8.385164807Subproblem 2
x + -3 = -5.385164807 Simplifying x + -3 = -5.385164807 Reorder the terms: -3 + x = -5.385164807 Solving -3 + x = -5.385164807 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 = -5.385164807 + 3 Combine like terms: -3 + 3 = 0 0 + x = -5.385164807 + 3 x = -5.385164807 + 3 Combine like terms: -5.385164807 + 3 = -2.385164807 x = -2.385164807 Simplifying x = -2.385164807Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.385164807, -2.385164807}
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