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Simplifying 2x2 + 31x + -9.1 = 0 Reorder the terms: -9.1 + 31x + 2x2 = 0 Solving -9.1 + 31x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4.55 + 15.5x + x2 = 0 Move the constant term to the right: Add '4.55' to each side of the equation. -4.55 + 15.5x + 4.55 + x2 = 0 + 4.55 Reorder the terms: -4.55 + 4.55 + 15.5x + x2 = 0 + 4.55 Combine like terms: -4.55 + 4.55 = 0.00 0.00 + 15.5x + x2 = 0 + 4.55 15.5x + x2 = 0 + 4.55 Combine like terms: 0 + 4.55 = 4.55 15.5x + x2 = 4.55 The x term is 15.5x. Take half its coefficient (7.75). Square it (60.0625) and add it to both sides. Add '60.0625' to each side of the equation. 15.5x + 60.0625 + x2 = 4.55 + 60.0625 Reorder the terms: 60.0625 + 15.5x + x2 = 4.55 + 60.0625 Combine like terms: 4.55 + 60.0625 = 64.6125 60.0625 + 15.5x + x2 = 64.6125 Factor a perfect square on the left side: (x + 7.75)(x + 7.75) = 64.6125 Calculate the square root of the right side: 8.038190095 Break this problem into two subproblems by setting (x + 7.75) equal to 8.038190095 and -8.038190095.Subproblem 1
x + 7.75 = 8.038190095 Simplifying x + 7.75 = 8.038190095 Reorder the terms: 7.75 + x = 8.038190095 Solving 7.75 + x = 8.038190095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.75' to each side of the equation. 7.75 + -7.75 + x = 8.038190095 + -7.75 Combine like terms: 7.75 + -7.75 = 0.00 0.00 + x = 8.038190095 + -7.75 x = 8.038190095 + -7.75 Combine like terms: 8.038190095 + -7.75 = 0.288190095 x = 0.288190095 Simplifying x = 0.288190095Subproblem 2
x + 7.75 = -8.038190095 Simplifying x + 7.75 = -8.038190095 Reorder the terms: 7.75 + x = -8.038190095 Solving 7.75 + x = -8.038190095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.75' to each side of the equation. 7.75 + -7.75 + x = -8.038190095 + -7.75 Combine like terms: 7.75 + -7.75 = 0.00 0.00 + x = -8.038190095 + -7.75 x = -8.038190095 + -7.75 Combine like terms: -8.038190095 + -7.75 = -15.788190095 x = -15.788190095 Simplifying x = -15.788190095Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.288190095, -15.788190095}
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