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Simplifying 7x2 + 17x + -9 = 0 Reorder the terms: -9 + 17x + 7x2 = 0 Solving -9 + 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'. -1.285714286 + 2.428571429x + x2 = 0 Move the constant term to the right: Add '1.285714286' to each side of the equation. -1.285714286 + 2.428571429x + 1.285714286 + x2 = 0 + 1.285714286 Reorder the terms: -1.285714286 + 1.285714286 + 2.428571429x + x2 = 0 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + 2.428571429x + x2 = 0 + 1.285714286 2.428571429x + x2 = 0 + 1.285714286 Combine like terms: 0 + 1.285714286 = 1.285714286 2.428571429x + x2 = 1.285714286 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 = 1.285714286 + 1.474489798 Reorder the terms: 1.474489798 + 2.428571429x + x2 = 1.285714286 + 1.474489798 Combine like terms: 1.285714286 + 1.474489798 = 2.760204084 1.474489798 + 2.428571429x + x2 = 2.760204084 Factor a perfect square on the left side: (x + 1.214285715)(x + 1.214285715) = 2.760204084 Calculate the square root of the right side: 1.661386194 Break this problem into two subproblems by setting (x + 1.214285715) equal to 1.661386194 and -1.661386194.Subproblem 1
x + 1.214285715 = 1.661386194 Simplifying x + 1.214285715 = 1.661386194 Reorder the terms: 1.214285715 + x = 1.661386194 Solving 1.214285715 + x = 1.661386194 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 = 1.661386194 + -1.214285715 Combine like terms: 1.214285715 + -1.214285715 = 0.000000000 0.000000000 + x = 1.661386194 + -1.214285715 x = 1.661386194 + -1.214285715 Combine like terms: 1.661386194 + -1.214285715 = 0.447100479 x = 0.447100479 Simplifying x = 0.447100479Subproblem 2
x + 1.214285715 = -1.661386194 Simplifying x + 1.214285715 = -1.661386194 Reorder the terms: 1.214285715 + x = -1.661386194 Solving 1.214285715 + x = -1.661386194 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 = -1.661386194 + -1.214285715 Combine like terms: 1.214285715 + -1.214285715 = 0.000000000 0.000000000 + x = -1.661386194 + -1.214285715 x = -1.661386194 + -1.214285715 Combine like terms: -1.661386194 + -1.214285715 = -2.875671909 x = -2.875671909 Simplifying x = -2.875671909Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.447100479, -2.875671909}
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