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Simplifying x2 + -41x = 400 + 0 Reorder the terms: -41x + x2 = 400 + 0 Combine like terms: 400 + 0 = 400 -41x + x2 = 400 Solving -41x + x2 = 400 Solving for variable 'x'. Reorder the terms: -400 + -41x + x2 = 400 + -400 Combine like terms: 400 + -400 = 0 -400 + -41x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '400' to each side of the equation. -400 + -41x + 400 + x2 = 0 + 400 Reorder the terms: -400 + 400 + -41x + x2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + -41x + x2 = 0 + 400 -41x + x2 = 0 + 400 Combine like terms: 0 + 400 = 400 -41x + x2 = 400 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 = 400 + 420.25 Reorder the terms: 420.25 + -41x + x2 = 400 + 420.25 Combine like terms: 400 + 420.25 = 820.25 420.25 + -41x + x2 = 820.25 Factor a perfect square on the left side: (x + -20.5)(x + -20.5) = 820.25 Calculate the square root of the right side: 28.640006983 Break this problem into two subproblems by setting (x + -20.5) equal to 28.640006983 and -28.640006983.Subproblem 1
x + -20.5 = 28.640006983 Simplifying x + -20.5 = 28.640006983 Reorder the terms: -20.5 + x = 28.640006983 Solving -20.5 + x = 28.640006983 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 = 28.640006983 + 20.5 Combine like terms: -20.5 + 20.5 = 0.0 0.0 + x = 28.640006983 + 20.5 x = 28.640006983 + 20.5 Combine like terms: 28.640006983 + 20.5 = 49.140006983 x = 49.140006983 Simplifying x = 49.140006983Subproblem 2
x + -20.5 = -28.640006983 Simplifying x + -20.5 = -28.640006983 Reorder the terms: -20.5 + x = -28.640006983 Solving -20.5 + x = -28.640006983 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 = -28.640006983 + 20.5 Combine like terms: -20.5 + 20.5 = 0.0 0.0 + x = -28.640006983 + 20.5 x = -28.640006983 + 20.5 Combine like terms: -28.640006983 + 20.5 = -8.140006983 x = -8.140006983 Simplifying x = -8.140006983Solution
The solution to the problem is based on the solutions from the subproblems. x = {49.140006983, -8.140006983}
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