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Simplifying 7X2 + -17X + -20 = 0 Reorder the terms: -20 + -17X + 7X2 = 0 Solving -20 + -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'. -2.857142857 + -2.428571429X + X2 = 0 Move the constant term to the right: Add '2.857142857' to each side of the equation. -2.857142857 + -2.428571429X + 2.857142857 + X2 = 0 + 2.857142857 Reorder the terms: -2.857142857 + 2.857142857 + -2.428571429X + X2 = 0 + 2.857142857 Combine like terms: -2.857142857 + 2.857142857 = 0.000000000 0.000000000 + -2.428571429X + X2 = 0 + 2.857142857 -2.428571429X + X2 = 0 + 2.857142857 Combine like terms: 0 + 2.857142857 = 2.857142857 -2.428571429X + X2 = 2.857142857 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 = 2.857142857 + 1.474489798 Reorder the terms: 1.474489798 + -2.428571429X + X2 = 2.857142857 + 1.474489798 Combine like terms: 2.857142857 + 1.474489798 = 4.331632655 1.474489798 + -2.428571429X + X2 = 4.331632655 Factor a perfect square on the left side: (X + -1.214285715)(X + -1.214285715) = 4.331632655 Calculate the square root of the right side: 2.08125747 Break this problem into two subproblems by setting (X + -1.214285715) equal to 2.08125747 and -2.08125747.Subproblem 1
X + -1.214285715 = 2.08125747 Simplifying X + -1.214285715 = 2.08125747 Reorder the terms: -1.214285715 + X = 2.08125747 Solving -1.214285715 + X = 2.08125747 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 = 2.08125747 + 1.214285715 Combine like terms: -1.214285715 + 1.214285715 = 0.000000000 0.000000000 + X = 2.08125747 + 1.214285715 X = 2.08125747 + 1.214285715 Combine like terms: 2.08125747 + 1.214285715 = 3.295543185 X = 3.295543185 Simplifying X = 3.295543185Subproblem 2
X + -1.214285715 = -2.08125747 Simplifying X + -1.214285715 = -2.08125747 Reorder the terms: -1.214285715 + X = -2.08125747 Solving -1.214285715 + X = -2.08125747 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 = -2.08125747 + 1.214285715 Combine like terms: -1.214285715 + 1.214285715 = 0.000000000 0.000000000 + X = -2.08125747 + 1.214285715 X = -2.08125747 + 1.214285715 Combine like terms: -2.08125747 + 1.214285715 = -0.866971755 X = -0.866971755 Simplifying X = -0.866971755Solution
The solution to the problem is based on the solutions from the subproblems. X = {3.295543185, -0.866971755}
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