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Simplifying 7x2 + 17x + -20 = -18 Reorder the terms: -20 + 17x + 7x2 = -18 Solving -20 + 17x + 7x2 = -18 Solving for variable 'x'. Reorder the terms: -20 + 18 + 17x + 7x2 = -18 + 18 Combine like terms: -20 + 18 = -2 -2 + 17x + 7x2 = -18 + 18 Combine like terms: -18 + 18 = 0 -2 + 17x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.2857142857 + 2.428571429x + x2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + 2.428571429x + 0.2857142857 + x2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + 2.428571429x + x2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + 2.428571429x + x2 = 0 + 0.2857142857 2.428571429x + x2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 2.428571429x + x2 = 0.2857142857 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 = 0.2857142857 + 1.474489798 Reorder the terms: 1.474489798 + 2.428571429x + x2 = 0.2857142857 + 1.474489798 Combine like terms: 0.2857142857 + 1.474489798 = 1.7602040837 1.474489798 + 2.428571429x + x2 = 1.7602040837 Factor a perfect square on the left side: (x + 1.214285715)(x + 1.214285715) = 1.7602040837 Calculate the square root of the right side: 1.326726831 Break this problem into two subproblems by setting (x + 1.214285715) equal to 1.326726831 and -1.326726831.Subproblem 1
x + 1.214285715 = 1.326726831 Simplifying x + 1.214285715 = 1.326726831 Reorder the terms: 1.214285715 + x = 1.326726831 Solving 1.214285715 + x = 1.326726831 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 = 1.326726831 + -1.214285715 Combine like terms: 1.214285715 + -1.214285715 = 0.000000000 0.000000000 + x = 1.326726831 + -1.214285715 x = 1.326726831 + -1.214285715 Combine like terms: 1.326726831 + -1.214285715 = 0.112441116 x = 0.112441116 Simplifying x = 0.112441116Subproblem 2
x + 1.214285715 = -1.326726831 Simplifying x + 1.214285715 = -1.326726831 Reorder the terms: 1.214285715 + x = -1.326726831 Solving 1.214285715 + x = -1.326726831 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 = -1.326726831 + -1.214285715 Combine like terms: 1.214285715 + -1.214285715 = 0.000000000 0.000000000 + x = -1.326726831 + -1.214285715 x = -1.326726831 + -1.214285715 Combine like terms: -1.326726831 + -1.214285715 = -2.541012546 x = -2.541012546 Simplifying x = -2.541012546Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.112441116, -2.541012546}
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