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Simplifying 35x2 + -12x + -27 = 0 Reorder the terms: -27 + -12x + 35x2 = 0 Solving -27 + -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'. -0.7714285714 + -0.3428571429x + x2 = 0 Move the constant term to the right: Add '0.7714285714' to each side of the equation. -0.7714285714 + -0.3428571429x + 0.7714285714 + x2 = 0 + 0.7714285714 Reorder the terms: -0.7714285714 + 0.7714285714 + -0.3428571429x + x2 = 0 + 0.7714285714 Combine like terms: -0.7714285714 + 0.7714285714 = 0.0000000000 0.0000000000 + -0.3428571429x + x2 = 0 + 0.7714285714 -0.3428571429x + x2 = 0 + 0.7714285714 Combine like terms: 0 + 0.7714285714 = 0.7714285714 -0.3428571429x + x2 = 0.7714285714 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 = 0.7714285714 + 0.02938775513 Reorder the terms: 0.02938775513 + -0.3428571429x + x2 = 0.7714285714 + 0.02938775513 Combine like terms: 0.7714285714 + 0.02938775513 = 0.80081632653 0.02938775513 + -0.3428571429x + x2 = 0.80081632653 Factor a perfect square on the left side: (x + -0.1714285715)(x + -0.1714285715) = 0.80081632653 Calculate the square root of the right side: 0.894883415 Break this problem into two subproblems by setting (x + -0.1714285715) equal to 0.894883415 and -0.894883415.Subproblem 1
x + -0.1714285715 = 0.894883415 Simplifying x + -0.1714285715 = 0.894883415 Reorder the terms: -0.1714285715 + x = 0.894883415 Solving -0.1714285715 + x = 0.894883415 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 = 0.894883415 + 0.1714285715 Combine like terms: -0.1714285715 + 0.1714285715 = 0.0000000000 0.0000000000 + x = 0.894883415 + 0.1714285715 x = 0.894883415 + 0.1714285715 Combine like terms: 0.894883415 + 0.1714285715 = 1.0663119865 x = 1.0663119865 Simplifying x = 1.0663119865Subproblem 2
x + -0.1714285715 = -0.894883415 Simplifying x + -0.1714285715 = -0.894883415 Reorder the terms: -0.1714285715 + x = -0.894883415 Solving -0.1714285715 + x = -0.894883415 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 = -0.894883415 + 0.1714285715 Combine like terms: -0.1714285715 + 0.1714285715 = 0.0000000000 0.0000000000 + x = -0.894883415 + 0.1714285715 x = -0.894883415 + 0.1714285715 Combine like terms: -0.894883415 + 0.1714285715 = -0.7234548435 x = -0.7234548435 Simplifying x = -0.7234548435Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0663119865, -0.7234548435}
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