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Simplifying 7x2 + 17x + -8 = 0 Reorder the terms: -8 + 17x + 7x2 = 0 Solving -8 + 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'. -1.142857143 + 2.428571429x + x2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + 2.428571429x + 1.142857143 + x2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + 2.428571429x + x2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + 2.428571429x + x2 = 0 + 1.142857143 2.428571429x + x2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 2.428571429x + x2 = 1.142857143 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 = 1.142857143 + 1.474489798 Reorder the terms: 1.474489798 + 2.428571429x + x2 = 1.142857143 + 1.474489798 Combine like terms: 1.142857143 + 1.474489798 = 2.617346941 1.474489798 + 2.428571429x + x2 = 2.617346941 Factor a perfect square on the left side: (x + 1.214285715)(x + 1.214285715) = 2.617346941 Calculate the square root of the right side: 1.617821665 Break this problem into two subproblems by setting (x + 1.214285715) equal to 1.617821665 and -1.617821665.Subproblem 1
x + 1.214285715 = 1.617821665 Simplifying x + 1.214285715 = 1.617821665 Reorder the terms: 1.214285715 + x = 1.617821665 Solving 1.214285715 + x = 1.617821665 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 = 1.617821665 + -1.214285715 Combine like terms: 1.214285715 + -1.214285715 = 0.000000000 0.000000000 + x = 1.617821665 + -1.214285715 x = 1.617821665 + -1.214285715 Combine like terms: 1.617821665 + -1.214285715 = 0.40353595 x = 0.40353595 Simplifying x = 0.40353595Subproblem 2
x + 1.214285715 = -1.617821665 Simplifying x + 1.214285715 = -1.617821665 Reorder the terms: 1.214285715 + x = -1.617821665 Solving 1.214285715 + x = -1.617821665 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 = -1.617821665 + -1.214285715 Combine like terms: 1.214285715 + -1.214285715 = 0.000000000 0.000000000 + x = -1.617821665 + -1.214285715 x = -1.617821665 + -1.214285715 Combine like terms: -1.617821665 + -1.214285715 = -2.83210738 x = -2.83210738 Simplifying x = -2.83210738Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.40353595, -2.83210738}
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