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Simplifying 7x2 + 59x + -29 = 0 Reorder the terms: -29 + 59x + 7x2 = 0 Solving -29 + 59x + 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'. -4.142857143 + 8.428571429x + x2 = 0 Move the constant term to the right: Add '4.142857143' to each side of the equation. -4.142857143 + 8.428571429x + 4.142857143 + x2 = 0 + 4.142857143 Reorder the terms: -4.142857143 + 4.142857143 + 8.428571429x + x2 = 0 + 4.142857143 Combine like terms: -4.142857143 + 4.142857143 = 0.000000000 0.000000000 + 8.428571429x + x2 = 0 + 4.142857143 8.428571429x + x2 = 0 + 4.142857143 Combine like terms: 0 + 4.142857143 = 4.142857143 8.428571429x + x2 = 4.142857143 The x term is 8.428571429x. Take half its coefficient (4.214285715). Square it (17.76020409) and add it to both sides. Add '17.76020409' to each side of the equation. 8.428571429x + 17.76020409 + x2 = 4.142857143 + 17.76020409 Reorder the terms: 17.76020409 + 8.428571429x + x2 = 4.142857143 + 17.76020409 Combine like terms: 4.142857143 + 17.76020409 = 21.903061233 17.76020409 + 8.428571429x + x2 = 21.903061233 Factor a perfect square on the left side: (x + 4.214285715)(x + 4.214285715) = 21.903061233 Calculate the square root of the right side: 4.680070644 Break this problem into two subproblems by setting (x + 4.214285715) equal to 4.680070644 and -4.680070644.Subproblem 1
x + 4.214285715 = 4.680070644 Simplifying x + 4.214285715 = 4.680070644 Reorder the terms: 4.214285715 + x = 4.680070644 Solving 4.214285715 + x = 4.680070644 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.214285715' to each side of the equation. 4.214285715 + -4.214285715 + x = 4.680070644 + -4.214285715 Combine like terms: 4.214285715 + -4.214285715 = 0.000000000 0.000000000 + x = 4.680070644 + -4.214285715 x = 4.680070644 + -4.214285715 Combine like terms: 4.680070644 + -4.214285715 = 0.465784929 x = 0.465784929 Simplifying x = 0.465784929Subproblem 2
x + 4.214285715 = -4.680070644 Simplifying x + 4.214285715 = -4.680070644 Reorder the terms: 4.214285715 + x = -4.680070644 Solving 4.214285715 + x = -4.680070644 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.214285715' to each side of the equation. 4.214285715 + -4.214285715 + x = -4.680070644 + -4.214285715 Combine like terms: 4.214285715 + -4.214285715 = 0.000000000 0.000000000 + x = -4.680070644 + -4.214285715 x = -4.680070644 + -4.214285715 Combine like terms: -4.680070644 + -4.214285715 = -8.894356359 x = -8.894356359 Simplifying x = -8.894356359Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.465784929, -8.894356359}
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