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Simplifying x2 + -41x = 8 Reorder the terms: -41x + x2 = 8 Solving -41x + x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + -41x + x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + -41x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -41x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -41x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -41x + x2 = 0 + 8 -41x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -41x + x2 = 8 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 = 8 + 420.25 Reorder the terms: 420.25 + -41x + x2 = 8 + 420.25 Combine like terms: 8 + 420.25 = 428.25 420.25 + -41x + x2 = 428.25 Factor a perfect square on the left side: (x + -20.5)(x + -20.5) = 428.25 Calculate the square root of the right side: 20.694202087 Break this problem into two subproblems by setting (x + -20.5) equal to 20.694202087 and -20.694202087.Subproblem 1
x + -20.5 = 20.694202087 Simplifying x + -20.5 = 20.694202087 Reorder the terms: -20.5 + x = 20.694202087 Solving -20.5 + x = 20.694202087 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 = 20.694202087 + 20.5 Combine like terms: -20.5 + 20.5 = 0.0 0.0 + x = 20.694202087 + 20.5 x = 20.694202087 + 20.5 Combine like terms: 20.694202087 + 20.5 = 41.194202087 x = 41.194202087 Simplifying x = 41.194202087Subproblem 2
x + -20.5 = -20.694202087 Simplifying x + -20.5 = -20.694202087 Reorder the terms: -20.5 + x = -20.694202087 Solving -20.5 + x = -20.694202087 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 = -20.694202087 + 20.5 Combine like terms: -20.5 + 20.5 = 0.0 0.0 + x = -20.694202087 + 20.5 x = -20.694202087 + 20.5 Combine like terms: -20.694202087 + 20.5 = -0.194202087 x = -0.194202087 Simplifying x = -0.194202087Solution
The solution to the problem is based on the solutions from the subproblems. x = {41.194202087, -0.194202087}
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