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Simplifying 2x2 + 16x + 31 = 2 Reorder the terms: 31 + 16x + 2x2 = 2 Solving 31 + 16x + 2x2 = 2 Solving for variable 'x'. Reorder the terms: 31 + -2 + 16x + 2x2 = 2 + -2 Combine like terms: 31 + -2 = 29 29 + 16x + 2x2 = 2 + -2 Combine like terms: 2 + -2 = 0 29 + 16x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 14.5 + 8x + x2 = 0 Move the constant term to the right: Add '-14.5' to each side of the equation. 14.5 + 8x + -14.5 + x2 = 0 + -14.5 Reorder the terms: 14.5 + -14.5 + 8x + x2 = 0 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + 8x + x2 = 0 + -14.5 8x + x2 = 0 + -14.5 Combine like terms: 0 + -14.5 = -14.5 8x + x2 = -14.5 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = -14.5 + 16 Reorder the terms: 16 + 8x + x2 = -14.5 + 16 Combine like terms: -14.5 + 16 = 1.5 16 + 8x + x2 = 1.5 Factor a perfect square on the left side: (x + 4)(x + 4) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (x + 4) equal to 1.224744871 and -1.224744871.Subproblem 1
x + 4 = 1.224744871 Simplifying x + 4 = 1.224744871 Reorder the terms: 4 + x = 1.224744871 Solving 4 + x = 1.224744871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 1.224744871 + -4 Combine like terms: 4 + -4 = 0 0 + x = 1.224744871 + -4 x = 1.224744871 + -4 Combine like terms: 1.224744871 + -4 = -2.775255129 x = -2.775255129 Simplifying x = -2.775255129Subproblem 2
x + 4 = -1.224744871 Simplifying x + 4 = -1.224744871 Reorder the terms: 4 + x = -1.224744871 Solving 4 + x = -1.224744871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -1.224744871 + -4 Combine like terms: 4 + -4 = 0 0 + x = -1.224744871 + -4 x = -1.224744871 + -4 Combine like terms: -1.224744871 + -4 = -5.224744871 x = -5.224744871 Simplifying x = -5.224744871Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.775255129, -5.224744871}
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