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Simplifying 37 + -11x = 81 + -1x2 Solving 37 + -11x = 81 + -1x2 Solving for variable 'x'. Reorder the terms: 37 + -81 + -11x + x2 = 81 + -1x2 + -81 + x2 Combine like terms: 37 + -81 = -44 -44 + -11x + x2 = 81 + -1x2 + -81 + x2 Reorder the terms: -44 + -11x + x2 = 81 + -81 + -1x2 + x2 Combine like terms: 81 + -81 = 0 -44 + -11x + x2 = 0 + -1x2 + x2 -44 + -11x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -44 + -11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '44' to each side of the equation. -44 + -11x + 44 + x2 = 0 + 44 Reorder the terms: -44 + 44 + -11x + x2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + -11x + x2 = 0 + 44 -11x + x2 = 0 + 44 Combine like terms: 0 + 44 = 44 -11x + x2 = 44 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = 44 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 44 + 30.25 Combine like terms: 44 + 30.25 = 74.25 30.25 + -11x + x2 = 74.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 74.25 Calculate the square root of the right side: 8.61684397 Break this problem into two subproblems by setting (x + -5.5) equal to 8.61684397 and -8.61684397.Subproblem 1
x + -5.5 = 8.61684397 Simplifying x + -5.5 = 8.61684397 Reorder the terms: -5.5 + x = 8.61684397 Solving -5.5 + x = 8.61684397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 8.61684397 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 8.61684397 + 5.5 x = 8.61684397 + 5.5 Combine like terms: 8.61684397 + 5.5 = 14.11684397 x = 14.11684397 Simplifying x = 14.11684397Subproblem 2
x + -5.5 = -8.61684397 Simplifying x + -5.5 = -8.61684397 Reorder the terms: -5.5 + x = -8.61684397 Solving -5.5 + x = -8.61684397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -8.61684397 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -8.61684397 + 5.5 x = -8.61684397 + 5.5 Combine like terms: -8.61684397 + 5.5 = -3.11684397 x = -3.11684397 Simplifying x = -3.11684397Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.11684397, -3.11684397}
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