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Simplifying x2 + -41x + -540 = 0 Reorder the terms: -540 + -41x + x2 = 0 Solving -540 + -41x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '540' to each side of the equation. -540 + -41x + 540 + x2 = 0 + 540 Reorder the terms: -540 + 540 + -41x + x2 = 0 + 540 Combine like terms: -540 + 540 = 0 0 + -41x + x2 = 0 + 540 -41x + x2 = 0 + 540 Combine like terms: 0 + 540 = 540 -41x + x2 = 540 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 = 540 + 420.25 Reorder the terms: 420.25 + -41x + x2 = 540 + 420.25 Combine like terms: 540 + 420.25 = 960.25 420.25 + -41x + x2 = 960.25 Factor a perfect square on the left side: (x + -20.5)(x + -20.5) = 960.25 Calculate the square root of the right side: 30.987900865 Break this problem into two subproblems by setting (x + -20.5) equal to 30.987900865 and -30.987900865.Subproblem 1
x + -20.5 = 30.987900865 Simplifying x + -20.5 = 30.987900865 Reorder the terms: -20.5 + x = 30.987900865 Solving -20.5 + x = 30.987900865 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 = 30.987900865 + 20.5 Combine like terms: -20.5 + 20.5 = 0.0 0.0 + x = 30.987900865 + 20.5 x = 30.987900865 + 20.5 Combine like terms: 30.987900865 + 20.5 = 51.487900865 x = 51.487900865 Simplifying x = 51.487900865Subproblem 2
x + -20.5 = -30.987900865 Simplifying x + -20.5 = -30.987900865 Reorder the terms: -20.5 + x = -30.987900865 Solving -20.5 + x = -30.987900865 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 = -30.987900865 + 20.5 Combine like terms: -20.5 + 20.5 = 0.0 0.0 + x = -30.987900865 + 20.5 x = -30.987900865 + 20.5 Combine like terms: -30.987900865 + 20.5 = -10.487900865 x = -10.487900865 Simplifying x = -10.487900865Solution
The solution to the problem is based on the solutions from the subproblems. x = {51.487900865, -10.487900865}
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