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Simplifying 35x2 + 12x + -35 = 0 Reorder the terms: -35 + 12x + 35x2 = 0 Solving -35 + 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 + 0.3428571429x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.3428571429x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 0.3428571429x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.3428571429x + x2 = 0 + 1 0.3428571429x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.3428571429x + x2 = 1 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 + 0.02938775513 Reorder the terms: 0.02938775513 + 0.3428571429x + x2 = 1 + 0.02938775513 Combine like terms: 1 + 0.02938775513 = 1.02938775513 0.02938775513 + 0.3428571429x + x2 = 1.02938775513 Factor a perfect square on the left side: (x + 0.1714285715)(x + 0.1714285715) = 1.02938775513 Calculate the square root of the right side: 1.01458748 Break this problem into two subproblems by setting (x + 0.1714285715) equal to 1.01458748 and -1.01458748.Subproblem 1
x + 0.1714285715 = 1.01458748 Simplifying x + 0.1714285715 = 1.01458748 Reorder the terms: 0.1714285715 + x = 1.01458748 Solving 0.1714285715 + x = 1.01458748 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 = 1.01458748 + -0.1714285715 Combine like terms: 0.1714285715 + -0.1714285715 = 0.0000000000 0.0000000000 + x = 1.01458748 + -0.1714285715 x = 1.01458748 + -0.1714285715 Combine like terms: 1.01458748 + -0.1714285715 = 0.8431589085 x = 0.8431589085 Simplifying x = 0.8431589085Subproblem 2
x + 0.1714285715 = -1.01458748 Simplifying x + 0.1714285715 = -1.01458748 Reorder the terms: 0.1714285715 + x = -1.01458748 Solving 0.1714285715 + x = -1.01458748 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 = -1.01458748 + -0.1714285715 Combine like terms: 0.1714285715 + -0.1714285715 = 0.0000000000 0.0000000000 + x = -1.01458748 + -0.1714285715 x = -1.01458748 + -0.1714285715 Combine like terms: -1.01458748 + -0.1714285715 = -1.1860160515 x = -1.1860160515 Simplifying x = -1.1860160515Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8431589085, -1.1860160515}
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