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Simplifying 7x2 + -17x + -42 = 0 Reorder the terms: -42 + -17x + 7x2 = 0 Solving -42 + -17x + 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'. -6 + -2.428571429x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -2.428571429x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -2.428571429x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -2.428571429x + x2 = 0 + 6 -2.428571429x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -2.428571429x + x2 = 6 The x term is -2.428571429x. Take half its coefficient (-1.214285715). Square it (1.474489798) and add it to both sides. Add '1.474489798' to each side of the equation. -2.428571429x + 1.474489798 + x2 = 6 + 1.474489798 Reorder the terms: 1.474489798 + -2.428571429x + x2 = 6 + 1.474489798 Combine like terms: 6 + 1.474489798 = 7.474489798 1.474489798 + -2.428571429x + x2 = 7.474489798 Factor a perfect square on the left side: (x + -1.214285715)(x + -1.214285715) = 7.474489798 Calculate the square root of the right side: 2.733951316 Break this problem into two subproblems by setting (x + -1.214285715) equal to 2.733951316 and -2.733951316.Subproblem 1
x + -1.214285715 = 2.733951316 Simplifying x + -1.214285715 = 2.733951316 Reorder the terms: -1.214285715 + x = 2.733951316 Solving -1.214285715 + x = 2.733951316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.214285715' to each side of the equation. -1.214285715 + 1.214285715 + x = 2.733951316 + 1.214285715 Combine like terms: -1.214285715 + 1.214285715 = 0.000000000 0.000000000 + x = 2.733951316 + 1.214285715 x = 2.733951316 + 1.214285715 Combine like terms: 2.733951316 + 1.214285715 = 3.948237031 x = 3.948237031 Simplifying x = 3.948237031Subproblem 2
x + -1.214285715 = -2.733951316 Simplifying x + -1.214285715 = -2.733951316 Reorder the terms: -1.214285715 + x = -2.733951316 Solving -1.214285715 + x = -2.733951316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.214285715' to each side of the equation. -1.214285715 + 1.214285715 + x = -2.733951316 + 1.214285715 Combine like terms: -1.214285715 + 1.214285715 = 0.000000000 0.000000000 + x = -2.733951316 + 1.214285715 x = -2.733951316 + 1.214285715 Combine like terms: -2.733951316 + 1.214285715 = -1.519665601 x = -1.519665601 Simplifying x = -1.519665601Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.948237031, -1.519665601}
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