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Simplifying 0.35x2 + -32.9x + 518 = 0 Reorder the terms: 518 + -32.9x + 0.35x2 = 0 Solving 518 + -32.9x + 0.35x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.35 the coefficient of the squared term: Divide each side by '0.35'. 1480 + -94x + x2 = 0 Move the constant term to the right: Add '-1480' to each side of the equation. 1480 + -94x + -1480 + x2 = 0 + -1480 Reorder the terms: 1480 + -1480 + -94x + x2 = 0 + -1480 Combine like terms: 1480 + -1480 = 0 0 + -94x + x2 = 0 + -1480 -94x + x2 = 0 + -1480 Combine like terms: 0 + -1480 = -1480 -94x + x2 = -1480 The x term is -94x. Take half its coefficient (-47). Square it (2209) and add it to both sides. Add '2209' to each side of the equation. -94x + 2209 + x2 = -1480 + 2209 Reorder the terms: 2209 + -94x + x2 = -1480 + 2209 Combine like terms: -1480 + 2209 = 729 2209 + -94x + x2 = 729 Factor a perfect square on the left side: (x + -47)(x + -47) = 729 Calculate the square root of the right side: 27 Break this problem into two subproblems by setting (x + -47) equal to 27 and -27.Subproblem 1
x + -47 = 27 Simplifying x + -47 = 27 Reorder the terms: -47 + x = 27 Solving -47 + x = 27 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '47' to each side of the equation. -47 + 47 + x = 27 + 47 Combine like terms: -47 + 47 = 0 0 + x = 27 + 47 x = 27 + 47 Combine like terms: 27 + 47 = 74 x = 74 Simplifying x = 74Subproblem 2
x + -47 = -27 Simplifying x + -47 = -27 Reorder the terms: -47 + x = -27 Solving -47 + x = -27 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '47' to each side of the equation. -47 + 47 + x = -27 + 47 Combine like terms: -47 + 47 = 0 0 + x = -27 + 47 x = -27 + 47 Combine like terms: -27 + 47 = 20 x = 20 Simplifying x = 20Solution
The solution to the problem is based on the solutions from the subproblems. x = {74, 20}
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