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Simplifying x4 + 9x2 + 16 = 1 Reorder the terms: 16 + 9x2 + x4 = 1 Solving 16 + 9x2 + x4 = 1 Solving for variable 'x'. Reorder the terms: 16 + -1 + 9x2 + x4 = 1 + -1 Combine like terms: 16 + -1 = 15 15 + 9x2 + x4 = 1 + -1 Combine like terms: 1 + -1 = 0 15 + 9x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + 9x2 + -15 + x4 = 0 + -15 Reorder the terms: 15 + -15 + 9x2 + x4 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 9x2 + x4 = 0 + -15 9x2 + x4 = 0 + -15 Combine like terms: 0 + -15 = -15 9x2 + x4 = -15 The x term is 9x2. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x2 + 20.25 + x4 = -15 + 20.25 Reorder the terms: 20.25 + 9x2 + x4 = -15 + 20.25 Combine like terms: -15 + 20.25 = 5.25 20.25 + 9x2 + x4 = 5.25 Factor a perfect square on the left side: (x2 + 4.5)(x2 + 4.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (x2 + 4.5) equal to 2.291287847 and -2.291287847.Subproblem 1
x2 + 4.5 = 2.291287847 Simplifying x2 + 4.5 = 2.291287847 Reorder the terms: 4.5 + x2 = 2.291287847 Solving 4.5 + x2 = 2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x2 = 2.291287847 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x2 = 2.291287847 + -4.5 x2 = 2.291287847 + -4.5 Combine like terms: 2.291287847 + -4.5 = -2.208712153 x2 = -2.208712153 Simplifying x2 = -2.208712153 Reorder the terms: 2.208712153 + x2 = -2.208712153 + 2.208712153 Combine like terms: -2.208712153 + 2.208712153 = 0.000000000 2.208712153 + 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 + 4.5 = -2.291287847 Simplifying x2 + 4.5 = -2.291287847 Reorder the terms: 4.5 + x2 = -2.291287847 Solving 4.5 + x2 = -2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x2 = -2.291287847 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x2 = -2.291287847 + -4.5 x2 = -2.291287847 + -4.5 Combine like terms: -2.291287847 + -4.5 = -6.791287847 x2 = -6.791287847 Simplifying x2 = -6.791287847 Reorder the terms: 6.791287847 + x2 = -6.791287847 + 6.791287847 Combine like terms: -6.791287847 + 6.791287847 = 0.000000000 6.791287847 + 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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