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Simplifying 5x4 + -8x2 + -3 = 0 Reorder the terms: -3 + -8x2 + 5x4 = 0 Solving -3 + -8x2 + 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'. -0.6 + -1.6x2 + x4 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -1.6x2 + 0.6 + x4 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -1.6x2 + x4 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -1.6x2 + x4 = 0 + 0.6 -1.6x2 + x4 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -1.6x2 + x4 = 0.6 The x term is -1.6x2. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6x2 + 0.64 + x4 = 0.6 + 0.64 Reorder the terms: 0.64 + -1.6x2 + x4 = 0.6 + 0.64 Combine like terms: 0.6 + 0.64 = 1.24 0.64 + -1.6x2 + x4 = 1.24 Factor a perfect square on the left side: (x2 + -0.8)(x2 + -0.8) = 1.24 Calculate the square root of the right side: 1.113552873 Break this problem into two subproblems by setting (x2 + -0.8) equal to 1.113552873 and -1.113552873.Subproblem 1
x2 + -0.8 = 1.113552873 Simplifying x2 + -0.8 = 1.113552873 Reorder the terms: -0.8 + x2 = 1.113552873 Solving -0.8 + x2 = 1.113552873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x2 = 1.113552873 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x2 = 1.113552873 + 0.8 x2 = 1.113552873 + 0.8 Combine like terms: 1.113552873 + 0.8 = 1.913552873 x2 = 1.913552873 Simplifying x2 = 1.913552873 Take the square root of each side: x = {-1.383312283, 1.383312283}Subproblem 2
x2 + -0.8 = -1.113552873 Simplifying x2 + -0.8 = -1.113552873 Reorder the terms: -0.8 + x2 = -1.113552873 Solving -0.8 + x2 = -1.113552873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x2 = -1.113552873 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x2 = -1.113552873 + 0.8 x2 = -1.113552873 + 0.8 Combine like terms: -1.113552873 + 0.8 = -0.313552873 x2 = -0.313552873 Simplifying x2 = -0.313552873 Reorder the terms: 0.313552873 + x2 = -0.313552873 + 0.313552873 Combine like terms: -0.313552873 + 0.313552873 = 0.000000000 0.313552873 + 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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