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Simplifying 2x4 + -22x2 + 41 = 0 Reorder the terms: 41 + -22x2 + 2x4 = 0 Solving 41 + -22x2 + 2x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 20.5 + -11x2 + x4 = 0 Move the constant term to the right: Add '-20.5' to each side of the equation. 20.5 + -11x2 + -20.5 + x4 = 0 + -20.5 Reorder the terms: 20.5 + -20.5 + -11x2 + x4 = 0 + -20.5 Combine like terms: 20.5 + -20.5 = 0.0 0.0 + -11x2 + x4 = 0 + -20.5 -11x2 + x4 = 0 + -20.5 Combine like terms: 0 + -20.5 = -20.5 -11x2 + x4 = -20.5 The x term is -11x2. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x2 + 30.25 + x4 = -20.5 + 30.25 Reorder the terms: 30.25 + -11x2 + x4 = -20.5 + 30.25 Combine like terms: -20.5 + 30.25 = 9.75 30.25 + -11x2 + x4 = 9.75 Factor a perfect square on the left side: (x2 + -5.5)(x2 + -5.5) = 9.75 Calculate the square root of the right side: 3.122498999 Break this problem into two subproblems by setting (x2 + -5.5) equal to 3.122498999 and -3.122498999.Subproblem 1
x2 + -5.5 = 3.122498999 Simplifying x2 + -5.5 = 3.122498999 Reorder the terms: -5.5 + x2 = 3.122498999 Solving -5.5 + x2 = 3.122498999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x2 = 3.122498999 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x2 = 3.122498999 + 5.5 x2 = 3.122498999 + 5.5 Combine like terms: 3.122498999 + 5.5 = 8.622498999 x2 = 8.622498999 Simplifying x2 = 8.622498999 Take the square root of each side: x = {-2.936409202, 2.936409202}Subproblem 2
x2 + -5.5 = -3.122498999 Simplifying x2 + -5.5 = -3.122498999 Reorder the terms: -5.5 + x2 = -3.122498999 Solving -5.5 + x2 = -3.122498999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x2 = -3.122498999 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x2 = -3.122498999 + 5.5 x2 = -3.122498999 + 5.5 Combine like terms: -3.122498999 + 5.5 = 2.377501001 x2 = 2.377501001 Simplifying x2 = 2.377501001 Take the square root of each side: x = {-1.541914719, 1.541914719}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.936409202, 2.936409202, -1.541914719, 1.541914719}
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