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Simplifying 0.9394 = (35 + x)(39 + x) Multiply (35 + x) * (39 + x) 0.9394 = (35(39 + x) + x(39 + x)) 0.9394 = ((39 * 35 + x * 35) + x(39 + x)) 0.9394 = ((1365 + 35x) + x(39 + x)) 0.9394 = (1365 + 35x + (39 * x + x * x)) 0.9394 = (1365 + 35x + (39x + x2)) Combine like terms: 35x + 39x = 74x 0.9394 = (1365 + 74x + x2) Solving 0.9394 = 1365 + 74x + x2 Solving for variable 'x'. Combine like terms: 0.9394 + -1365 = -1364.0606 -1364.0606 + -74x + -1x2 = 1365 + 74x + x2 + -1365 + -74x + -1x2 Reorder the terms: -1364.0606 + -74x + -1x2 = 1365 + -1365 + 74x + -74x + x2 + -1x2 Combine like terms: 1365 + -1365 = 0 -1364.0606 + -74x + -1x2 = 0 + 74x + -74x + x2 + -1x2 -1364.0606 + -74x + -1x2 = 74x + -74x + x2 + -1x2 Combine like terms: 74x + -74x = 0 -1364.0606 + -74x + -1x2 = 0 + x2 + -1x2 -1364.0606 + -74x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -1364.0606 + -74x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1364.0606 + 74x + x2 = 0 Move the constant term to the right: Add '-1364.0606' to each side of the equation. 1364.0606 + 74x + -1364.0606 + x2 = 0 + -1364.0606 Reorder the terms: 1364.0606 + -1364.0606 + 74x + x2 = 0 + -1364.0606 Combine like terms: 1364.0606 + -1364.0606 = 0.0000 0.0000 + 74x + x2 = 0 + -1364.0606 74x + x2 = 0 + -1364.0606 Combine like terms: 0 + -1364.0606 = -1364.0606 74x + x2 = -1364.0606 The x term is 74x. Take half its coefficient (37). Square it (1369) and add it to both sides. Add '1369' to each side of the equation. 74x + 1369 + x2 = -1364.0606 + 1369 Reorder the terms: 1369 + 74x + x2 = -1364.0606 + 1369 Combine like terms: -1364.0606 + 1369 = 4.9394 1369 + 74x + x2 = 4.9394 Factor a perfect square on the left side: (x + 37)(x + 37) = 4.9394 Calculate the square root of the right side: 2.222476097 Break this problem into two subproblems by setting (x + 37) equal to 2.222476097 and -2.222476097.Subproblem 1
x + 37 = 2.222476097 Simplifying x + 37 = 2.222476097 Reorder the terms: 37 + x = 2.222476097 Solving 37 + x = 2.222476097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-37' to each side of the equation. 37 + -37 + x = 2.222476097 + -37 Combine like terms: 37 + -37 = 0 0 + x = 2.222476097 + -37 x = 2.222476097 + -37 Combine like terms: 2.222476097 + -37 = -34.777523903 x = -34.777523903 Simplifying x = -34.777523903Subproblem 2
x + 37 = -2.222476097 Simplifying x + 37 = -2.222476097 Reorder the terms: 37 + x = -2.222476097 Solving 37 + x = -2.222476097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-37' to each side of the equation. 37 + -37 + x = -2.222476097 + -37 Combine like terms: 37 + -37 = 0 0 + x = -2.222476097 + -37 x = -2.222476097 + -37 Combine like terms: -2.222476097 + -37 = -39.222476097 x = -39.222476097 Simplifying x = -39.222476097Solution
The solution to the problem is based on the solutions from the subproblems. x = {-34.777523903, -39.222476097}
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