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Simplifying 7x2 + 17x + -11 = 0 Reorder the terms: -11 + 17x + 7x2 = 0 Solving -11 + 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'. -1.571428571 + 2.428571429x + x2 = 0 Move the constant term to the right: Add '1.571428571' to each side of the equation. -1.571428571 + 2.428571429x + 1.571428571 + x2 = 0 + 1.571428571 Reorder the terms: -1.571428571 + 1.571428571 + 2.428571429x + x2 = 0 + 1.571428571 Combine like terms: -1.571428571 + 1.571428571 = 0.000000000 0.000000000 + 2.428571429x + x2 = 0 + 1.571428571 2.428571429x + x2 = 0 + 1.571428571 Combine like terms: 0 + 1.571428571 = 1.571428571 2.428571429x + x2 = 1.571428571 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 = 1.571428571 + 1.474489798 Reorder the terms: 1.474489798 + 2.428571429x + x2 = 1.571428571 + 1.474489798 Combine like terms: 1.571428571 + 1.474489798 = 3.045918369 1.474489798 + 2.428571429x + x2 = 3.045918369 Factor a perfect square on the left side: (x + 1.214285715)(x + 1.214285715) = 3.045918369 Calculate the square root of the right side: 1.745255961 Break this problem into two subproblems by setting (x + 1.214285715) equal to 1.745255961 and -1.745255961.Subproblem 1
x + 1.214285715 = 1.745255961 Simplifying x + 1.214285715 = 1.745255961 Reorder the terms: 1.214285715 + x = 1.745255961 Solving 1.214285715 + x = 1.745255961 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 = 1.745255961 + -1.214285715 Combine like terms: 1.214285715 + -1.214285715 = 0.000000000 0.000000000 + x = 1.745255961 + -1.214285715 x = 1.745255961 + -1.214285715 Combine like terms: 1.745255961 + -1.214285715 = 0.530970246 x = 0.530970246 Simplifying x = 0.530970246Subproblem 2
x + 1.214285715 = -1.745255961 Simplifying x + 1.214285715 = -1.745255961 Reorder the terms: 1.214285715 + x = -1.745255961 Solving 1.214285715 + x = -1.745255961 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 = -1.745255961 + -1.214285715 Combine like terms: 1.214285715 + -1.214285715 = 0.000000000 0.000000000 + x = -1.745255961 + -1.214285715 x = -1.745255961 + -1.214285715 Combine like terms: -1.745255961 + -1.214285715 = -2.959541676 x = -2.959541676 Simplifying x = -2.959541676Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.530970246, -2.959541676}
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