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Simplifying 35x2 + -12x + -49 = 0 Reorder the terms: -49 + -12x + 35x2 = 0 Solving -49 + -12x + 35x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -1.4 + -0.3428571429x + x2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + -0.3428571429x + 1.4 + x2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + -0.3428571429x + x2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + -0.3428571429x + x2 = 0 + 1.4 -0.3428571429x + x2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 -0.3428571429x + x2 = 1.4 The x term is -0.3428571429x. Take half its coefficient (-0.1714285715). Square it (0.02938775513) and add it to both sides. Add '0.02938775513' to each side of the equation. -0.3428571429x + 0.02938775513 + x2 = 1.4 + 0.02938775513 Reorder the terms: 0.02938775513 + -0.3428571429x + x2 = 1.4 + 0.02938775513 Combine like terms: 1.4 + 0.02938775513 = 1.42938775513 0.02938775513 + -0.3428571429x + x2 = 1.42938775513 Factor a perfect square on the left side: (x + -0.1714285715)(x + -0.1714285715) = 1.42938775513 Calculate the square root of the right side: 1.195570054 Break this problem into two subproblems by setting (x + -0.1714285715) equal to 1.195570054 and -1.195570054.Subproblem 1
x + -0.1714285715 = 1.195570054 Simplifying x + -0.1714285715 = 1.195570054 Reorder the terms: -0.1714285715 + x = 1.195570054 Solving -0.1714285715 + x = 1.195570054 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1714285715' to each side of the equation. -0.1714285715 + 0.1714285715 + x = 1.195570054 + 0.1714285715 Combine like terms: -0.1714285715 + 0.1714285715 = 0.0000000000 0.0000000000 + x = 1.195570054 + 0.1714285715 x = 1.195570054 + 0.1714285715 Combine like terms: 1.195570054 + 0.1714285715 = 1.3669986255 x = 1.3669986255 Simplifying x = 1.3669986255Subproblem 2
x + -0.1714285715 = -1.195570054 Simplifying x + -0.1714285715 = -1.195570054 Reorder the terms: -0.1714285715 + x = -1.195570054 Solving -0.1714285715 + x = -1.195570054 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1714285715' to each side of the equation. -0.1714285715 + 0.1714285715 + x = -1.195570054 + 0.1714285715 Combine like terms: -0.1714285715 + 0.1714285715 = 0.0000000000 0.0000000000 + x = -1.195570054 + 0.1714285715 x = -1.195570054 + 0.1714285715 Combine like terms: -1.195570054 + 0.1714285715 = -1.0241414825 x = -1.0241414825 Simplifying x = -1.0241414825Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3669986255, -1.0241414825}
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