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Simplifying 35x2 + -13 = 4x Reorder the terms: -13 + 35x2 = 4x Solving -13 + 35x2 = 4x Solving for variable 'x'. Reorder the terms: -13 + -4x + 35x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -13 + -4x + 35x2 = 0 Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -0.3714285714 + -0.1142857143x + x2 = 0 Move the constant term to the right: Add '0.3714285714' to each side of the equation. -0.3714285714 + -0.1142857143x + 0.3714285714 + x2 = 0 + 0.3714285714 Reorder the terms: -0.3714285714 + 0.3714285714 + -0.1142857143x + x2 = 0 + 0.3714285714 Combine like terms: -0.3714285714 + 0.3714285714 = 0.0000000000 0.0000000000 + -0.1142857143x + x2 = 0 + 0.3714285714 -0.1142857143x + x2 = 0 + 0.3714285714 Combine like terms: 0 + 0.3714285714 = 0.3714285714 -0.1142857143x + x2 = 0.3714285714 The x term is -0.1142857143x. Take half its coefficient (-0.05714285715). Square it (0.003265306123) and add it to both sides. Add '0.003265306123' to each side of the equation. -0.1142857143x + 0.003265306123 + x2 = 0.3714285714 + 0.003265306123 Reorder the terms: 0.003265306123 + -0.1142857143x + x2 = 0.3714285714 + 0.003265306123 Combine like terms: 0.3714285714 + 0.003265306123 = 0.374693877523 0.003265306123 + -0.1142857143x + x2 = 0.374693877523 Factor a perfect square on the left side: (x + -0.05714285715)(x + -0.05714285715) = 0.374693877523 Calculate the square root of the right side: 0.612122437 Break this problem into two subproblems by setting (x + -0.05714285715) equal to 0.612122437 and -0.612122437.Subproblem 1
x + -0.05714285715 = 0.612122437 Simplifying x + -0.05714285715 = 0.612122437 Reorder the terms: -0.05714285715 + x = 0.612122437 Solving -0.05714285715 + x = 0.612122437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05714285715' to each side of the equation. -0.05714285715 + 0.05714285715 + x = 0.612122437 + 0.05714285715 Combine like terms: -0.05714285715 + 0.05714285715 = 0.00000000000 0.00000000000 + x = 0.612122437 + 0.05714285715 x = 0.612122437 + 0.05714285715 Combine like terms: 0.612122437 + 0.05714285715 = 0.66926529415 x = 0.66926529415 Simplifying x = 0.66926529415Subproblem 2
x + -0.05714285715 = -0.612122437 Simplifying x + -0.05714285715 = -0.612122437 Reorder the terms: -0.05714285715 + x = -0.612122437 Solving -0.05714285715 + x = -0.612122437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05714285715' to each side of the equation. -0.05714285715 + 0.05714285715 + x = -0.612122437 + 0.05714285715 Combine like terms: -0.05714285715 + 0.05714285715 = 0.00000000000 0.00000000000 + x = -0.612122437 + 0.05714285715 x = -0.612122437 + 0.05714285715 Combine like terms: -0.612122437 + 0.05714285715 = -0.55497957985 x = -0.55497957985 Simplifying x = -0.55497957985Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.66926529415, -0.55497957985}
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