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Simplifying 7x2 + -17x + -5 = 0 Reorder the terms: -5 + -17x + 7x2 = 0 Solving -5 + -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'. -0.7142857143 + -2.428571429x + x2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + -2.428571429x + 0.7142857143 + x2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + -2.428571429x + x2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + -2.428571429x + x2 = 0 + 0.7142857143 -2.428571429x + x2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 -2.428571429x + x2 = 0.7142857143 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 = 0.7142857143 + 1.474489798 Reorder the terms: 1.474489798 + -2.428571429x + x2 = 0.7142857143 + 1.474489798 Combine like terms: 0.7142857143 + 1.474489798 = 2.1887755123 1.474489798 + -2.428571429x + x2 = 2.1887755123 Factor a perfect square on the left side: (x + -1.214285715)(x + -1.214285715) = 2.1887755123 Calculate the square root of the right side: 1.479451085 Break this problem into two subproblems by setting (x + -1.214285715) equal to 1.479451085 and -1.479451085.Subproblem 1
x + -1.214285715 = 1.479451085 Simplifying x + -1.214285715 = 1.479451085 Reorder the terms: -1.214285715 + x = 1.479451085 Solving -1.214285715 + x = 1.479451085 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 = 1.479451085 + 1.214285715 Combine like terms: -1.214285715 + 1.214285715 = 0.000000000 0.000000000 + x = 1.479451085 + 1.214285715 x = 1.479451085 + 1.214285715 Combine like terms: 1.479451085 + 1.214285715 = 2.6937368 x = 2.6937368 Simplifying x = 2.6937368Subproblem 2
x + -1.214285715 = -1.479451085 Simplifying x + -1.214285715 = -1.479451085 Reorder the terms: -1.214285715 + x = -1.479451085 Solving -1.214285715 + x = -1.479451085 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 = -1.479451085 + 1.214285715 Combine like terms: -1.214285715 + 1.214285715 = 0.000000000 0.000000000 + x = -1.479451085 + 1.214285715 x = -1.479451085 + 1.214285715 Combine like terms: -1.479451085 + 1.214285715 = -0.26516537 x = -0.26516537 Simplifying x = -0.26516537Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.6937368, -0.26516537}
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