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Simplifying x(43 + 56x) = 34 (43 * x + 56x * x) = 34 (43x + 56x2) = 34 Solving 43x + 56x2 = 34 Solving for variable 'x'. Reorder the terms: -34 + 43x + 56x2 = 34 + -34 Combine like terms: 34 + -34 = 0 -34 + 43x + 56x2 = 0 Begin completing the square. Divide all terms by 56 the coefficient of the squared term: Divide each side by '56'. -0.6071428571 + 0.7678571429x + x2 = 0 Move the constant term to the right: Add '0.6071428571' to each side of the equation. -0.6071428571 + 0.7678571429x + 0.6071428571 + x2 = 0 + 0.6071428571 Reorder the terms: -0.6071428571 + 0.6071428571 + 0.7678571429x + x2 = 0 + 0.6071428571 Combine like terms: -0.6071428571 + 0.6071428571 = 0.0000000000 0.0000000000 + 0.7678571429x + x2 = 0 + 0.6071428571 0.7678571429x + x2 = 0 + 0.6071428571 Combine like terms: 0 + 0.6071428571 = 0.6071428571 0.7678571429x + x2 = 0.6071428571 The x term is 0.7678571429x. Take half its coefficient (0.3839285715). Square it (0.1474011480) and add it to both sides. Add '0.1474011480' to each side of the equation. 0.7678571429x + 0.1474011480 + x2 = 0.6071428571 + 0.1474011480 Reorder the terms: 0.1474011480 + 0.7678571429x + x2 = 0.6071428571 + 0.1474011480 Combine like terms: 0.6071428571 + 0.1474011480 = 0.7545440051 0.1474011480 + 0.7678571429x + x2 = 0.7545440051 Factor a perfect square on the left side: (x + 0.3839285715)(x + 0.3839285715) = 0.7545440051 Calculate the square root of the right side: 0.868644925 Break this problem into two subproblems by setting (x + 0.3839285715) equal to 0.868644925 and -0.868644925.Subproblem 1
x + 0.3839285715 = 0.868644925 Simplifying x + 0.3839285715 = 0.868644925 Reorder the terms: 0.3839285715 + x = 0.868644925 Solving 0.3839285715 + x = 0.868644925 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3839285715' to each side of the equation. 0.3839285715 + -0.3839285715 + x = 0.868644925 + -0.3839285715 Combine like terms: 0.3839285715 + -0.3839285715 = 0.0000000000 0.0000000000 + x = 0.868644925 + -0.3839285715 x = 0.868644925 + -0.3839285715 Combine like terms: 0.868644925 + -0.3839285715 = 0.4847163535 x = 0.4847163535 Simplifying x = 0.4847163535Subproblem 2
x + 0.3839285715 = -0.868644925 Simplifying x + 0.3839285715 = -0.868644925 Reorder the terms: 0.3839285715 + x = -0.868644925 Solving 0.3839285715 + x = -0.868644925 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3839285715' to each side of the equation. 0.3839285715 + -0.3839285715 + x = -0.868644925 + -0.3839285715 Combine like terms: 0.3839285715 + -0.3839285715 = 0.0000000000 0.0000000000 + x = -0.868644925 + -0.3839285715 x = -0.868644925 + -0.3839285715 Combine like terms: -0.868644925 + -0.3839285715 = -1.2525734965 x = -1.2525734965 Simplifying x = -1.2525734965Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4847163535, -1.2525734965}
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