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Simplifying (x4) + 9(x2) + 11 = 0 x4 + 9(x2) + 11 = 0 Reorder the terms: 11 + 9x2 + x4 = 0 Solving 11 + 9x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + 9x2 + -11 + x4 = 0 + -11 Reorder the terms: 11 + -11 + 9x2 + x4 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 9x2 + x4 = 0 + -11 9x2 + x4 = 0 + -11 Combine like terms: 0 + -11 = -11 9x2 + x4 = -11 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 = -11 + 20.25 Reorder the terms: 20.25 + 9x2 + x4 = -11 + 20.25 Combine like terms: -11 + 20.25 = 9.25 20.25 + 9x2 + x4 = 9.25 Factor a perfect square on the left side: (x2 + 4.5)(x2 + 4.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (x2 + 4.5) equal to 3.041381265 and -3.041381265.Subproblem 1
x2 + 4.5 = 3.041381265 Simplifying x2 + 4.5 = 3.041381265 Reorder the terms: 4.5 + x2 = 3.041381265 Solving 4.5 + x2 = 3.041381265 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 = 3.041381265 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x2 = 3.041381265 + -4.5 x2 = 3.041381265 + -4.5 Combine like terms: 3.041381265 + -4.5 = -1.458618735 x2 = -1.458618735 Simplifying x2 = -1.458618735 Reorder the terms: 1.458618735 + x2 = -1.458618735 + 1.458618735 Combine like terms: -1.458618735 + 1.458618735 = 0.000000000 1.458618735 + 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 = -3.041381265 Simplifying x2 + 4.5 = -3.041381265 Reorder the terms: 4.5 + x2 = -3.041381265 Solving 4.5 + x2 = -3.041381265 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 = -3.041381265 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x2 = -3.041381265 + -4.5 x2 = -3.041381265 + -4.5 Combine like terms: -3.041381265 + -4.5 = -7.541381265 x2 = -7.541381265 Simplifying x2 = -7.541381265 Reorder the terms: 7.541381265 + x2 = -7.541381265 + 7.541381265 Combine like terms: -7.541381265 + 7.541381265 = 0.000000000 7.541381265 + 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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