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Simplifying x2 + -80x + -1350 = 0 Reorder the terms: -1350 + -80x + x2 = 0 Solving -1350 + -80x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1350' to each side of the equation. -1350 + -80x + 1350 + x2 = 0 + 1350 Reorder the terms: -1350 + 1350 + -80x + x2 = 0 + 1350 Combine like terms: -1350 + 1350 = 0 0 + -80x + x2 = 0 + 1350 -80x + x2 = 0 + 1350 Combine like terms: 0 + 1350 = 1350 -80x + x2 = 1350 The x term is -80x. Take half its coefficient (-40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. -80x + 1600 + x2 = 1350 + 1600 Reorder the terms: 1600 + -80x + x2 = 1350 + 1600 Combine like terms: 1350 + 1600 = 2950 1600 + -80x + x2 = 2950 Factor a perfect square on the left side: (x + -40)(x + -40) = 2950 Calculate the square root of the right side: 54.313902456 Break this problem into two subproblems by setting (x + -40) equal to 54.313902456 and -54.313902456.Subproblem 1
x + -40 = 54.313902456 Simplifying x + -40 = 54.313902456 Reorder the terms: -40 + x = 54.313902456 Solving -40 + x = 54.313902456 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = 54.313902456 + 40 Combine like terms: -40 + 40 = 0 0 + x = 54.313902456 + 40 x = 54.313902456 + 40 Combine like terms: 54.313902456 + 40 = 94.313902456 x = 94.313902456 Simplifying x = 94.313902456Subproblem 2
x + -40 = -54.313902456 Simplifying x + -40 = -54.313902456 Reorder the terms: -40 + x = -54.313902456 Solving -40 + x = -54.313902456 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = -54.313902456 + 40 Combine like terms: -40 + 40 = 0 0 + x = -54.313902456 + 40 x = -54.313902456 + 40 Combine like terms: -54.313902456 + 40 = -14.313902456 x = -14.313902456 Simplifying x = -14.313902456Solution
The solution to the problem is based on the solutions from the subproblems. x = {94.313902456, -14.313902456}
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