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Simplifying x2 + -80x + -600 = 0 Reorder the terms: -600 + -80x + x2 = 0 Solving -600 + -80x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '600' to each side of the equation. -600 + -80x + 600 + x2 = 0 + 600 Reorder the terms: -600 + 600 + -80x + x2 = 0 + 600 Combine like terms: -600 + 600 = 0 0 + -80x + x2 = 0 + 600 -80x + x2 = 0 + 600 Combine like terms: 0 + 600 = 600 -80x + x2 = 600 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 = 600 + 1600 Reorder the terms: 1600 + -80x + x2 = 600 + 1600 Combine like terms: 600 + 1600 = 2200 1600 + -80x + x2 = 2200 Factor a perfect square on the left side: (x + -40)(x + -40) = 2200 Calculate the square root of the right side: 46.904157598 Break this problem into two subproblems by setting (x + -40) equal to 46.904157598 and -46.904157598.Subproblem 1
x + -40 = 46.904157598 Simplifying x + -40 = 46.904157598 Reorder the terms: -40 + x = 46.904157598 Solving -40 + x = 46.904157598 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 = 46.904157598 + 40 Combine like terms: -40 + 40 = 0 0 + x = 46.904157598 + 40 x = 46.904157598 + 40 Combine like terms: 46.904157598 + 40 = 86.904157598 x = 86.904157598 Simplifying x = 86.904157598Subproblem 2
x + -40 = -46.904157598 Simplifying x + -40 = -46.904157598 Reorder the terms: -40 + x = -46.904157598 Solving -40 + x = -46.904157598 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 = -46.904157598 + 40 Combine like terms: -40 + 40 = 0 0 + x = -46.904157598 + 40 x = -46.904157598 + 40 Combine like terms: -46.904157598 + 40 = -6.904157598 x = -6.904157598 Simplifying x = -6.904157598Solution
The solution to the problem is based on the solutions from the subproblems. x = {86.904157598, -6.904157598}
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