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Simplifying x2 + -153x + 3000 = 0 Reorder the terms: 3000 + -153x + x2 = 0 Solving 3000 + -153x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-3000' to each side of the equation. 3000 + -153x + -3000 + x2 = 0 + -3000 Reorder the terms: 3000 + -3000 + -153x + x2 = 0 + -3000 Combine like terms: 3000 + -3000 = 0 0 + -153x + x2 = 0 + -3000 -153x + x2 = 0 + -3000 Combine like terms: 0 + -3000 = -3000 -153x + x2 = -3000 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 = -3000 + 5852.25 Reorder the terms: 5852.25 + -153x + x2 = -3000 + 5852.25 Combine like terms: -3000 + 5852.25 = 2852.25 5852.25 + -153x + x2 = 2852.25 Factor a perfect square on the left side: (x + -76.5)(x + -76.5) = 2852.25 Calculate the square root of the right side: 53.406460283 Break this problem into two subproblems by setting (x + -76.5) equal to 53.406460283 and -53.406460283.Subproblem 1
x + -76.5 = 53.406460283 Simplifying x + -76.5 = 53.406460283 Reorder the terms: -76.5 + x = 53.406460283 Solving -76.5 + x = 53.406460283 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 = 53.406460283 + 76.5 Combine like terms: -76.5 + 76.5 = 0.0 0.0 + x = 53.406460283 + 76.5 x = 53.406460283 + 76.5 Combine like terms: 53.406460283 + 76.5 = 129.906460283 x = 129.906460283 Simplifying x = 129.906460283Subproblem 2
x + -76.5 = -53.406460283 Simplifying x + -76.5 = -53.406460283 Reorder the terms: -76.5 + x = -53.406460283 Solving -76.5 + x = -53.406460283 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 = -53.406460283 + 76.5 Combine like terms: -76.5 + 76.5 = 0.0 0.0 + x = -53.406460283 + 76.5 x = -53.406460283 + 76.5 Combine like terms: -53.406460283 + 76.5 = 23.093539717 x = 23.093539717 Simplifying x = 23.093539717Solution
The solution to the problem is based on the solutions from the subproblems. x = {129.906460283, 23.093539717}
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