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Simplifying 60x2 + 19x + -181 = 0 Reorder the terms: -181 + 19x + 60x2 = 0 Solving -181 + 19x + 60x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 60 the coefficient of the squared term: Divide each side by '60'. -3.016666667 + 0.3166666667x + x2 = 0 Move the constant term to the right: Add '3.016666667' to each side of the equation. -3.016666667 + 0.3166666667x + 3.016666667 + x2 = 0 + 3.016666667 Reorder the terms: -3.016666667 + 3.016666667 + 0.3166666667x + x2 = 0 + 3.016666667 Combine like terms: -3.016666667 + 3.016666667 = 0.000000000 0.000000000 + 0.3166666667x + x2 = 0 + 3.016666667 0.3166666667x + x2 = 0 + 3.016666667 Combine like terms: 0 + 3.016666667 = 3.016666667 0.3166666667x + x2 = 3.016666667 The x term is 0.3166666667x. Take half its coefficient (0.1583333334). Square it (0.02506944447) and add it to both sides. Add '0.02506944447' to each side of the equation. 0.3166666667x + 0.02506944447 + x2 = 3.016666667 + 0.02506944447 Reorder the terms: 0.02506944447 + 0.3166666667x + x2 = 3.016666667 + 0.02506944447 Combine like terms: 3.016666667 + 0.02506944447 = 3.04173611147 0.02506944447 + 0.3166666667x + x2 = 3.04173611147 Factor a perfect square on the left side: (x + 0.1583333334)(x + 0.1583333334) = 3.04173611147 Calculate the square root of the right side: 1.74405737 Break this problem into two subproblems by setting (x + 0.1583333334) equal to 1.74405737 and -1.74405737.Subproblem 1
x + 0.1583333334 = 1.74405737 Simplifying x + 0.1583333334 = 1.74405737 Reorder the terms: 0.1583333334 + x = 1.74405737 Solving 0.1583333334 + x = 1.74405737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1583333334' to each side of the equation. 0.1583333334 + -0.1583333334 + x = 1.74405737 + -0.1583333334 Combine like terms: 0.1583333334 + -0.1583333334 = 0.0000000000 0.0000000000 + x = 1.74405737 + -0.1583333334 x = 1.74405737 + -0.1583333334 Combine like terms: 1.74405737 + -0.1583333334 = 1.5857240366 x = 1.5857240366 Simplifying x = 1.5857240366Subproblem 2
x + 0.1583333334 = -1.74405737 Simplifying x + 0.1583333334 = -1.74405737 Reorder the terms: 0.1583333334 + x = -1.74405737 Solving 0.1583333334 + x = -1.74405737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1583333334' to each side of the equation. 0.1583333334 + -0.1583333334 + x = -1.74405737 + -0.1583333334 Combine like terms: 0.1583333334 + -0.1583333334 = 0.0000000000 0.0000000000 + x = -1.74405737 + -0.1583333334 x = -1.74405737 + -0.1583333334 Combine like terms: -1.74405737 + -0.1583333334 = -1.9023907034 x = -1.9023907034 Simplifying x = -1.9023907034Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5857240366, -1.9023907034}
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