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Simplifying x2 + 41x = 96 Reorder the terms: 41x + x2 = 96 Solving 41x + x2 = 96 Solving for variable 'x'. Reorder the terms: -96 + 41x + x2 = 96 + -96 Combine like terms: 96 + -96 = 0 -96 + 41x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '96' to each side of the equation. -96 + 41x + 96 + x2 = 0 + 96 Reorder the terms: -96 + 96 + 41x + x2 = 0 + 96 Combine like terms: -96 + 96 = 0 0 + 41x + x2 = 0 + 96 41x + x2 = 0 + 96 Combine like terms: 0 + 96 = 96 41x + x2 = 96 The x term is 41x. Take half its coefficient (20.5). Square it (420.25) and add it to both sides. Add '420.25' to each side of the equation. 41x + 420.25 + x2 = 96 + 420.25 Reorder the terms: 420.25 + 41x + x2 = 96 + 420.25 Combine like terms: 96 + 420.25 = 516.25 420.25 + 41x + x2 = 516.25 Factor a perfect square on the left side: (x + 20.5)(x + 20.5) = 516.25 Calculate the square root of the right side: 22.721135535 Break this problem into two subproblems by setting (x + 20.5) equal to 22.721135535 and -22.721135535.Subproblem 1
x + 20.5 = 22.721135535 Simplifying x + 20.5 = 22.721135535 Reorder the terms: 20.5 + x = 22.721135535 Solving 20.5 + x = 22.721135535 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20.5' to each side of the equation. 20.5 + -20.5 + x = 22.721135535 + -20.5 Combine like terms: 20.5 + -20.5 = 0.0 0.0 + x = 22.721135535 + -20.5 x = 22.721135535 + -20.5 Combine like terms: 22.721135535 + -20.5 = 2.221135535 x = 2.221135535 Simplifying x = 2.221135535Subproblem 2
x + 20.5 = -22.721135535 Simplifying x + 20.5 = -22.721135535 Reorder the terms: 20.5 + x = -22.721135535 Solving 20.5 + x = -22.721135535 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20.5' to each side of the equation. 20.5 + -20.5 + x = -22.721135535 + -20.5 Combine like terms: 20.5 + -20.5 = 0.0 0.0 + x = -22.721135535 + -20.5 x = -22.721135535 + -20.5 Combine like terms: -22.721135535 + -20.5 = -43.221135535 x = -43.221135535 Simplifying x = -43.221135535Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.221135535, -43.221135535}
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