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Simplifying 14x2 + -34x + 14 = 0 Reorder the terms: 14 + -34x + 14x2 = 0 Solving 14 + -34x + 14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(7 + -17x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + -17x + 7x2)' equal to zero and attempt to solve: Simplifying 7 + -17x + 7x2 = 0 Solving 7 + -17x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1 + -2.428571429x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -2.428571429x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -2.428571429x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2.428571429x + x2 = 0 + -1 -2.428571429x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2.428571429x + x2 = -1 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 + 1.474489798 Reorder the terms: 1.474489798 + -2.428571429x + x2 = -1 + 1.474489798 Combine like terms: -1 + 1.474489798 = 0.474489798 1.474489798 + -2.428571429x + x2 = 0.474489798 Factor a perfect square on the left side: (x + -1.214285715)(x + -1.214285715) = 0.474489798 Calculate the square root of the right side: 0.688832199 Break this problem into two subproblems by setting (x + -1.214285715) equal to 0.688832199 and -0.688832199.Subproblem 1
x + -1.214285715 = 0.688832199 Simplifying x + -1.214285715 = 0.688832199 Reorder the terms: -1.214285715 + x = 0.688832199 Solving -1.214285715 + x = 0.688832199 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 = 0.688832199 + 1.214285715 Combine like terms: -1.214285715 + 1.214285715 = 0.000000000 0.000000000 + x = 0.688832199 + 1.214285715 x = 0.688832199 + 1.214285715 Combine like terms: 0.688832199 + 1.214285715 = 1.903117914 x = 1.903117914 Simplifying x = 1.903117914Subproblem 2
x + -1.214285715 = -0.688832199 Simplifying x + -1.214285715 = -0.688832199 Reorder the terms: -1.214285715 + x = -0.688832199 Solving -1.214285715 + x = -0.688832199 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 = -0.688832199 + 1.214285715 Combine like terms: -1.214285715 + 1.214285715 = 0.000000000 0.000000000 + x = -0.688832199 + 1.214285715 x = -0.688832199 + 1.214285715 Combine like terms: -0.688832199 + 1.214285715 = 0.525453516 x = 0.525453516 Simplifying x = 0.525453516Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.903117914, 0.525453516}Solution
x = {1.903117914, 0.525453516}
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