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Simplifying 5x4 + -2x2 + -20x2 + -8 = 0 Reorder the terms: -8 + -2x2 + -20x2 + 5x4 = 0 Combine like terms: -2x2 + -20x2 = -22x2 -8 + -22x2 + 5x4 = 0 Solving -8 + -22x2 + 5x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.6 + -4.4x2 + x4 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + -4.4x2 + 1.6 + x4 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + -4.4x2 + x4 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + -4.4x2 + x4 = 0 + 1.6 -4.4x2 + x4 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 -4.4x2 + x4 = 1.6 The x term is -4.4x2. Take half its coefficient (-2.2). Square it (4.84) and add it to both sides. Add '4.84' to each side of the equation. -4.4x2 + 4.84 + x4 = 1.6 + 4.84 Reorder the terms: 4.84 + -4.4x2 + x4 = 1.6 + 4.84 Combine like terms: 1.6 + 4.84 = 6.44 4.84 + -4.4x2 + x4 = 6.44 Factor a perfect square on the left side: (x2 + -2.2)(x2 + -2.2) = 6.44 Calculate the square root of the right side: 2.537715508 Break this problem into two subproblems by setting (x2 + -2.2) equal to 2.537715508 and -2.537715508.Subproblem 1
x2 + -2.2 = 2.537715508 Simplifying x2 + -2.2 = 2.537715508 Reorder the terms: -2.2 + x2 = 2.537715508 Solving -2.2 + x2 = 2.537715508 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.2' to each side of the equation. -2.2 + 2.2 + x2 = 2.537715508 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + x2 = 2.537715508 + 2.2 x2 = 2.537715508 + 2.2 Combine like terms: 2.537715508 + 2.2 = 4.737715508 x2 = 4.737715508 Simplifying x2 = 4.737715508 Take the square root of each side: x = {-2.176629392, 2.176629392}Subproblem 2
x2 + -2.2 = -2.537715508 Simplifying x2 + -2.2 = -2.537715508 Reorder the terms: -2.2 + x2 = -2.537715508 Solving -2.2 + x2 = -2.537715508 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.2' to each side of the equation. -2.2 + 2.2 + x2 = -2.537715508 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + x2 = -2.537715508 + 2.2 x2 = -2.537715508 + 2.2 Combine like terms: -2.537715508 + 2.2 = -0.337715508 x2 = -0.337715508 Simplifying x2 = -0.337715508 Reorder the terms: 0.337715508 + x2 = -0.337715508 + 0.337715508 Combine like terms: -0.337715508 + 0.337715508 = 0.000000000 0.337715508 + 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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