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Simplifying x2 + 41x + 14 = 0 Reorder the terms: 14 + 41x + x2 = 0 Solving 14 + 41x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + 41x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + 41x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 41x + x2 = 0 + -14 41x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 41x + x2 = -14 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 = -14 + 420.25 Reorder the terms: 420.25 + 41x + x2 = -14 + 420.25 Combine like terms: -14 + 420.25 = 406.25 420.25 + 41x + x2 = 406.25 Factor a perfect square on the left side: (x + 20.5)(x + 20.5) = 406.25 Calculate the square root of the right side: 20.155644371 Break this problem into two subproblems by setting (x + 20.5) equal to 20.155644371 and -20.155644371.Subproblem 1
x + 20.5 = 20.155644371 Simplifying x + 20.5 = 20.155644371 Reorder the terms: 20.5 + x = 20.155644371 Solving 20.5 + x = 20.155644371 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 = 20.155644371 + -20.5 Combine like terms: 20.5 + -20.5 = 0.0 0.0 + x = 20.155644371 + -20.5 x = 20.155644371 + -20.5 Combine like terms: 20.155644371 + -20.5 = -0.344355629 x = -0.344355629 Simplifying x = -0.344355629Subproblem 2
x + 20.5 = -20.155644371 Simplifying x + 20.5 = -20.155644371 Reorder the terms: 20.5 + x = -20.155644371 Solving 20.5 + x = -20.155644371 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 = -20.155644371 + -20.5 Combine like terms: 20.5 + -20.5 = 0.0 0.0 + x = -20.155644371 + -20.5 x = -20.155644371 + -20.5 Combine like terms: -20.155644371 + -20.5 = -40.655644371 x = -40.655644371 Simplifying x = -40.655644371Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.344355629, -40.655644371}
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