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Simplifying x = x2 + -152x + 5791 Reorder the terms: x = 5791 + -152x + x2 Solving x = 5791 + -152x + x2 Solving for variable 'x'. Reorder the terms: -5791 + x + 152x + -1x2 = 5791 + -152x + x2 + -5791 + 152x + -1x2 Combine like terms: x + 152x = 153x -5791 + 153x + -1x2 = 5791 + -152x + x2 + -5791 + 152x + -1x2 Reorder the terms: -5791 + 153x + -1x2 = 5791 + -5791 + -152x + 152x + x2 + -1x2 Combine like terms: 5791 + -5791 = 0 -5791 + 153x + -1x2 = 0 + -152x + 152x + x2 + -1x2 -5791 + 153x + -1x2 = -152x + 152x + x2 + -1x2 Combine like terms: -152x + 152x = 0 -5791 + 153x + -1x2 = 0 + x2 + -1x2 -5791 + 153x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -5791 + 153x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 5791 + -153x + x2 = 0 Move the constant term to the right: Add '-5791' to each side of the equation. 5791 + -153x + -5791 + x2 = 0 + -5791 Reorder the terms: 5791 + -5791 + -153x + x2 = 0 + -5791 Combine like terms: 5791 + -5791 = 0 0 + -153x + x2 = 0 + -5791 -153x + x2 = 0 + -5791 Combine like terms: 0 + -5791 = -5791 -153x + x2 = -5791 The x term is -153x. Take half its coefficient (-76.5). Square it (5852.25) and add it to both sides. Add '5852.25' to each side of the equation. -153x + 5852.25 + x2 = -5791 + 5852.25 Reorder the terms: 5852.25 + -153x + x2 = -5791 + 5852.25 Combine like terms: -5791 + 5852.25 = 61.25 5852.25 + -153x + x2 = 61.25 Factor a perfect square on the left side: (x + -76.5)(x + -76.5) = 61.25 Calculate the square root of the right side: 7.826237921 Break this problem into two subproblems by setting (x + -76.5) equal to 7.826237921 and -7.826237921.Subproblem 1
x + -76.5 = 7.826237921 Simplifying x + -76.5 = 7.826237921 Reorder the terms: -76.5 + x = 7.826237921 Solving -76.5 + x = 7.826237921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '76.5' to each side of the equation. -76.5 + 76.5 + x = 7.826237921 + 76.5 Combine like terms: -76.5 + 76.5 = 0.0 0.0 + x = 7.826237921 + 76.5 x = 7.826237921 + 76.5 Combine like terms: 7.826237921 + 76.5 = 84.326237921 x = 84.326237921 Simplifying x = 84.326237921Subproblem 2
x + -76.5 = -7.826237921 Simplifying x + -76.5 = -7.826237921 Reorder the terms: -76.5 + x = -7.826237921 Solving -76.5 + x = -7.826237921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '76.5' to each side of the equation. -76.5 + 76.5 + x = -7.826237921 + 76.5 Combine like terms: -76.5 + 76.5 = 0.0 0.0 + x = -7.826237921 + 76.5 x = -7.826237921 + 76.5 Combine like terms: -7.826237921 + 76.5 = 68.673762079 x = 68.673762079 Simplifying x = 68.673762079Solution
The solution to the problem is based on the solutions from the subproblems. x = {84.326237921, 68.673762079}
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