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Simplifying x2 + -81x + 1600 = 0 Reorder the terms: 1600 + -81x + x2 = 0 Solving 1600 + -81x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1600' to each side of the equation. 1600 + -81x + -1600 + x2 = 0 + -1600 Reorder the terms: 1600 + -1600 + -81x + x2 = 0 + -1600 Combine like terms: 1600 + -1600 = 0 0 + -81x + x2 = 0 + -1600 -81x + x2 = 0 + -1600 Combine like terms: 0 + -1600 = -1600 -81x + x2 = -1600 The x term is -81x. Take half its coefficient (-40.5). Square it (1640.25) and add it to both sides. Add '1640.25' to each side of the equation. -81x + 1640.25 + x2 = -1600 + 1640.25 Reorder the terms: 1640.25 + -81x + x2 = -1600 + 1640.25 Combine like terms: -1600 + 1640.25 = 40.25 1640.25 + -81x + x2 = 40.25 Factor a perfect square on the left side: (x + -40.5)(x + -40.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (x + -40.5) equal to 6.34428877 and -6.34428877.Subproblem 1
x + -40.5 = 6.34428877 Simplifying x + -40.5 = 6.34428877 Reorder the terms: -40.5 + x = 6.34428877 Solving -40.5 + x = 6.34428877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40.5' to each side of the equation. -40.5 + 40.5 + x = 6.34428877 + 40.5 Combine like terms: -40.5 + 40.5 = 0.0 0.0 + x = 6.34428877 + 40.5 x = 6.34428877 + 40.5 Combine like terms: 6.34428877 + 40.5 = 46.84428877 x = 46.84428877 Simplifying x = 46.84428877Subproblem 2
x + -40.5 = -6.34428877 Simplifying x + -40.5 = -6.34428877 Reorder the terms: -40.5 + x = -6.34428877 Solving -40.5 + x = -6.34428877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40.5' to each side of the equation. -40.5 + 40.5 + x = -6.34428877 + 40.5 Combine like terms: -40.5 + 40.5 = 0.0 0.0 + x = -6.34428877 + 40.5 x = -6.34428877 + 40.5 Combine like terms: -6.34428877 + 40.5 = 34.15571123 x = 34.15571123 Simplifying x = 34.15571123Solution
The solution to the problem is based on the solutions from the subproblems. x = {46.84428877, 34.15571123}
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