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Simplifying 7x2 + -31x + -20 + -140 = 0 Reorder the terms: -20 + -140 + -31x + 7x2 = 0 Combine like terms: -20 + -140 = -160 -160 + -31x + 7x2 = 0 Solving -160 + -31x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -22.85714286 + -4.428571429x + x2 = 0 Move the constant term to the right: Add '22.85714286' to each side of the equation. -22.85714286 + -4.428571429x + 22.85714286 + x2 = 0 + 22.85714286 Reorder the terms: -22.85714286 + 22.85714286 + -4.428571429x + x2 = 0 + 22.85714286 Combine like terms: -22.85714286 + 22.85714286 = 0.00000000 0.00000000 + -4.428571429x + x2 = 0 + 22.85714286 -4.428571429x + x2 = 0 + 22.85714286 Combine like terms: 0 + 22.85714286 = 22.85714286 -4.428571429x + x2 = 22.85714286 The x term is -4.428571429x. Take half its coefficient (-2.214285715). Square it (4.903061228) and add it to both sides. Add '4.903061228' to each side of the equation. -4.428571429x + 4.903061228 + x2 = 22.85714286 + 4.903061228 Reorder the terms: 4.903061228 + -4.428571429x + x2 = 22.85714286 + 4.903061228 Combine like terms: 22.85714286 + 4.903061228 = 27.760204088 4.903061228 + -4.428571429x + x2 = 27.760204088 Factor a perfect square on the left side: (x + -2.214285715)(x + -2.214285715) = 27.760204088 Calculate the square root of the right side: 5.268795317 Break this problem into two subproblems by setting (x + -2.214285715) equal to 5.268795317 and -5.268795317.Subproblem 1
x + -2.214285715 = 5.268795317 Simplifying x + -2.214285715 = 5.268795317 Reorder the terms: -2.214285715 + x = 5.268795317 Solving -2.214285715 + x = 5.268795317 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.214285715' to each side of the equation. -2.214285715 + 2.214285715 + x = 5.268795317 + 2.214285715 Combine like terms: -2.214285715 + 2.214285715 = 0.000000000 0.000000000 + x = 5.268795317 + 2.214285715 x = 5.268795317 + 2.214285715 Combine like terms: 5.268795317 + 2.214285715 = 7.483081032 x = 7.483081032 Simplifying x = 7.483081032Subproblem 2
x + -2.214285715 = -5.268795317 Simplifying x + -2.214285715 = -5.268795317 Reorder the terms: -2.214285715 + x = -5.268795317 Solving -2.214285715 + x = -5.268795317 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.214285715' to each side of the equation. -2.214285715 + 2.214285715 + x = -5.268795317 + 2.214285715 Combine like terms: -2.214285715 + 2.214285715 = 0.000000000 0.000000000 + x = -5.268795317 + 2.214285715 x = -5.268795317 + 2.214285715 Combine like terms: -5.268795317 + 2.214285715 = -3.054509602 x = -3.054509602 Simplifying x = -3.054509602Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.483081032, -3.054509602}
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