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Simplifying 4x4 + 8x2 + 1 = 0 Reorder the terms: 1 + 8x2 + 4x4 = 0 Solving 1 + 8x2 + 4x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.25 + 2x2 + x4 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 2x2 + -0.25 + x4 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 2x2 + x4 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 2x2 + x4 = 0 + -0.25 2x2 + x4 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 2x2 + x4 = -0.25 The x term is 2x2. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x2 + 1 + x4 = -0.25 + 1 Reorder the terms: 1 + 2x2 + x4 = -0.25 + 1 Combine like terms: -0.25 + 1 = 0.75 1 + 2x2 + x4 = 0.75 Factor a perfect square on the left side: (x2 + 1)(x2 + 1) = 0.75 Calculate the square root of the right side: 0.866025404 Break this problem into two subproblems by setting (x2 + 1) equal to 0.866025404 and -0.866025404.Subproblem 1
x2 + 1 = 0.866025404 Simplifying x2 + 1 = 0.866025404 Reorder the terms: 1 + x2 = 0.866025404 Solving 1 + x2 = 0.866025404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x2 = 0.866025404 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = 0.866025404 + -1 x2 = 0.866025404 + -1 Combine like terms: 0.866025404 + -1 = -0.133974596 x2 = -0.133974596 Simplifying x2 = -0.133974596 Reorder the terms: 0.133974596 + x2 = -0.133974596 + 0.133974596 Combine like terms: -0.133974596 + 0.133974596 = 0.000000000 0.133974596 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x2 + 1 = -0.866025404 Simplifying x2 + 1 = -0.866025404 Reorder the terms: 1 + x2 = -0.866025404 Solving 1 + x2 = -0.866025404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x2 = -0.866025404 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = -0.866025404 + -1 x2 = -0.866025404 + -1 Combine like terms: -0.866025404 + -1 = -1.866025404 x2 = -1.866025404 Simplifying x2 = -1.866025404 Reorder the terms: 1.866025404 + x2 = -1.866025404 + 1.866025404 Combine like terms: -1.866025404 + 1.866025404 = 0.000000000 1.866025404 + 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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