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Simplifying -49x2 + 4606x + -52000 = 0 Reorder the terms: -52000 + 4606x + -49x2 = 0 Solving -52000 + 4606x + -49x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -49 the coefficient of the squared term: Divide each side by '-49'. 1061.22449 + -94x + x2 = 0 Move the constant term to the right: Add '-1061.22449' to each side of the equation. 1061.22449 + -94x + -1061.22449 + x2 = 0 + -1061.22449 Reorder the terms: 1061.22449 + -1061.22449 + -94x + x2 = 0 + -1061.22449 Combine like terms: 1061.22449 + -1061.22449 = 0.00000 0.00000 + -94x + x2 = 0 + -1061.22449 -94x + x2 = 0 + -1061.22449 Combine like terms: 0 + -1061.22449 = -1061.22449 -94x + x2 = -1061.22449 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 = -1061.22449 + 2209 Reorder the terms: 2209 + -94x + x2 = -1061.22449 + 2209 Combine like terms: -1061.22449 + 2209 = 1147.77551 2209 + -94x + x2 = 1147.77551 Factor a perfect square on the left side: (x + -47)(x + -47) = 1147.77551 Calculate the square root of the right side: 33.878835724 Break this problem into two subproblems by setting (x + -47) equal to 33.878835724 and -33.878835724.Subproblem 1
x + -47 = 33.878835724 Simplifying x + -47 = 33.878835724 Reorder the terms: -47 + x = 33.878835724 Solving -47 + x = 33.878835724 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 = 33.878835724 + 47 Combine like terms: -47 + 47 = 0 0 + x = 33.878835724 + 47 x = 33.878835724 + 47 Combine like terms: 33.878835724 + 47 = 80.878835724 x = 80.878835724 Simplifying x = 80.878835724Subproblem 2
x + -47 = -33.878835724 Simplifying x + -47 = -33.878835724 Reorder the terms: -47 + x = -33.878835724 Solving -47 + x = -33.878835724 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 = -33.878835724 + 47 Combine like terms: -47 + 47 = 0 0 + x = -33.878835724 + 47 x = -33.878835724 + 47 Combine like terms: -33.878835724 + 47 = 13.121164276 x = 13.121164276 Simplifying x = 13.121164276Solution
The solution to the problem is based on the solutions from the subproblems. x = {80.878835724, 13.121164276}
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