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Simplifying 5x4 + 2x2 + -8 = 0 Reorder the terms: -8 + 2x2 + 5x4 = 0 Solving -8 + 2x2 + 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 + 0.4x2 + x4 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + 0.4x2 + 1.6 + x4 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + 0.4x2 + x4 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + 0.4x2 + x4 = 0 + 1.6 0.4x2 + x4 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 0.4x2 + x4 = 1.6 The x term is 0.4x2. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x2 + 0.04 + x4 = 1.6 + 0.04 Reorder the terms: 0.04 + 0.4x2 + x4 = 1.6 + 0.04 Combine like terms: 1.6 + 0.04 = 1.64 0.04 + 0.4x2 + x4 = 1.64 Factor a perfect square on the left side: (x2 + 0.2)(x2 + 0.2) = 1.64 Calculate the square root of the right side: 1.280624847 Break this problem into two subproblems by setting (x2 + 0.2) equal to 1.280624847 and -1.280624847.Subproblem 1
x2 + 0.2 = 1.280624847 Simplifying x2 + 0.2 = 1.280624847 Reorder the terms: 0.2 + x2 = 1.280624847 Solving 0.2 + x2 = 1.280624847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x2 = 1.280624847 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x2 = 1.280624847 + -0.2 x2 = 1.280624847 + -0.2 Combine like terms: 1.280624847 + -0.2 = 1.080624847 x2 = 1.080624847 Simplifying x2 = 1.080624847 Take the square root of each side: x = {-1.039531071, 1.039531071}Subproblem 2
x2 + 0.2 = -1.280624847 Simplifying x2 + 0.2 = -1.280624847 Reorder the terms: 0.2 + x2 = -1.280624847 Solving 0.2 + x2 = -1.280624847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x2 = -1.280624847 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x2 = -1.280624847 + -0.2 x2 = -1.280624847 + -0.2 Combine like terms: -1.280624847 + -0.2 = -1.480624847 x2 = -1.480624847 Simplifying x2 = -1.480624847 Reorder the terms: 1.480624847 + x2 = -1.480624847 + 1.480624847 Combine like terms: -1.480624847 + 1.480624847 = 0.000000000 1.480624847 + 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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