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Simplifying 20x4 + -11x2 = 2 Reorder the terms: -11x2 + 20x4 = 2 Solving -11x2 + 20x4 = 2 Solving for variable 'x'. Reorder the terms: -2 + -11x2 + 20x4 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -11x2 + 20x4 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.1 + -0.55x2 + x4 = 0 Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + -0.55x2 + 0.1 + x4 = 0 + 0.1 Reorder the terms: -0.1 + 0.1 + -0.55x2 + x4 = 0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + -0.55x2 + x4 = 0 + 0.1 -0.55x2 + x4 = 0 + 0.1 Combine like terms: 0 + 0.1 = 0.1 -0.55x2 + x4 = 0.1 The x term is -0.55x2. Take half its coefficient (-0.275). Square it (0.075625) and add it to both sides. Add '0.075625' to each side of the equation. -0.55x2 + 0.075625 + x4 = 0.1 + 0.075625 Reorder the terms: 0.075625 + -0.55x2 + x4 = 0.1 + 0.075625 Combine like terms: 0.1 + 0.075625 = 0.175625 0.075625 + -0.55x2 + x4 = 0.175625 Factor a perfect square on the left side: (x2 + -0.275)(x2 + -0.275) = 0.175625 Calculate the square root of the right side: 0.419076365 Break this problem into two subproblems by setting (x2 + -0.275) equal to 0.419076365 and -0.419076365.Subproblem 1
x2 + -0.275 = 0.419076365 Simplifying x2 + -0.275 = 0.419076365 Reorder the terms: -0.275 + x2 = 0.419076365 Solving -0.275 + x2 = 0.419076365 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.275' to each side of the equation. -0.275 + 0.275 + x2 = 0.419076365 + 0.275 Combine like terms: -0.275 + 0.275 = 0.000 0.000 + x2 = 0.419076365 + 0.275 x2 = 0.419076365 + 0.275 Combine like terms: 0.419076365 + 0.275 = 0.694076365 x2 = 0.694076365 Simplifying x2 = 0.694076365 Take the square root of each side: x = {-0.833112456, 0.833112456}Subproblem 2
x2 + -0.275 = -0.419076365 Simplifying x2 + -0.275 = -0.419076365 Reorder the terms: -0.275 + x2 = -0.419076365 Solving -0.275 + x2 = -0.419076365 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.275' to each side of the equation. -0.275 + 0.275 + x2 = -0.419076365 + 0.275 Combine like terms: -0.275 + 0.275 = 0.000 0.000 + x2 = -0.419076365 + 0.275 x2 = -0.419076365 + 0.275 Combine like terms: -0.419076365 + 0.275 = -0.144076365 x2 = -0.144076365 Simplifying x2 = -0.144076365 Reorder the terms: 0.144076365 + x2 = -0.144076365 + 0.144076365 Combine like terms: -0.144076365 + 0.144076365 = 0.000000000 0.144076365 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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