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Simplifying 31x2 + -49x + -60 = 0 Reorder the terms: -60 + -49x + 31x2 = 0 Solving -60 + -49x + 31x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 31 the coefficient of the squared term: Divide each side by '31'. -1.935483871 + -1.580645161x + x2 = 0 Move the constant term to the right: Add '1.935483871' to each side of the equation. -1.935483871 + -1.580645161x + 1.935483871 + x2 = 0 + 1.935483871 Reorder the terms: -1.935483871 + 1.935483871 + -1.580645161x + x2 = 0 + 1.935483871 Combine like terms: -1.935483871 + 1.935483871 = 0.000000000 0.000000000 + -1.580645161x + x2 = 0 + 1.935483871 -1.580645161x + x2 = 0 + 1.935483871 Combine like terms: 0 + 1.935483871 = 1.935483871 -1.580645161x + x2 = 1.935483871 The x term is -1.580645161x. Take half its coefficient (-0.7903225805). Square it (0.6246097812) and add it to both sides. Add '0.6246097812' to each side of the equation. -1.580645161x + 0.6246097812 + x2 = 1.935483871 + 0.6246097812 Reorder the terms: 0.6246097812 + -1.580645161x + x2 = 1.935483871 + 0.6246097812 Combine like terms: 1.935483871 + 0.6246097812 = 2.5600936522 0.6246097812 + -1.580645161x + x2 = 2.5600936522 Factor a perfect square on the left side: (x + -0.7903225805)(x + -0.7903225805) = 2.5600936522 Calculate the square root of the right side: 1.600029266 Break this problem into two subproblems by setting (x + -0.7903225805) equal to 1.600029266 and -1.600029266.Subproblem 1
x + -0.7903225805 = 1.600029266 Simplifying x + -0.7903225805 = 1.600029266 Reorder the terms: -0.7903225805 + x = 1.600029266 Solving -0.7903225805 + x = 1.600029266 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7903225805' to each side of the equation. -0.7903225805 + 0.7903225805 + x = 1.600029266 + 0.7903225805 Combine like terms: -0.7903225805 + 0.7903225805 = 0.0000000000 0.0000000000 + x = 1.600029266 + 0.7903225805 x = 1.600029266 + 0.7903225805 Combine like terms: 1.600029266 + 0.7903225805 = 2.3903518465 x = 2.3903518465 Simplifying x = 2.3903518465Subproblem 2
x + -0.7903225805 = -1.600029266 Simplifying x + -0.7903225805 = -1.600029266 Reorder the terms: -0.7903225805 + x = -1.600029266 Solving -0.7903225805 + x = -1.600029266 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7903225805' to each side of the equation. -0.7903225805 + 0.7903225805 + x = -1.600029266 + 0.7903225805 Combine like terms: -0.7903225805 + 0.7903225805 = 0.0000000000 0.0000000000 + x = -1.600029266 + 0.7903225805 x = -1.600029266 + 0.7903225805 Combine like terms: -1.600029266 + 0.7903225805 = -0.8097066855 x = -0.8097066855 Simplifying x = -0.8097066855Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.3903518465, -0.8097066855}
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