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Simplifying x4 + -1x2 + 9 = 27 Reorder the terms: 9 + -1x2 + x4 = 27 Solving 9 + -1x2 + x4 = 27 Solving for variable 'x'. Reorder the terms: 9 + -27 + -1x2 + x4 = 27 + -27 Combine like terms: 9 + -27 = -18 -18 + -1x2 + x4 = 27 + -27 Combine like terms: 27 + -27 = 0 -18 + -1x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + -1x2 + 18 + x4 = 0 + 18 Reorder the terms: -18 + 18 + -1x2 + x4 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -1x2 + x4 = 0 + 18 -1x2 + x4 = 0 + 18 Combine like terms: 0 + 18 = 18 -1x2 + x4 = 18 The x term is -1x2. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x2 + 0.25 + x4 = 18 + 0.25 Reorder the terms: 0.25 + -1x2 + x4 = 18 + 0.25 Combine like terms: 18 + 0.25 = 18.25 0.25 + -1x2 + x4 = 18.25 Factor a perfect square on the left side: (x2 + -0.5)(x2 + -0.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (x2 + -0.5) equal to 4.272001873 and -4.272001873.Subproblem 1
x2 + -0.5 = 4.272001873 Simplifying x2 + -0.5 = 4.272001873 Reorder the terms: -0.5 + x2 = 4.272001873 Solving -0.5 + x2 = 4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x2 = 4.272001873 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = 4.272001873 + 0.5 x2 = 4.272001873 + 0.5 Combine like terms: 4.272001873 + 0.5 = 4.772001873 x2 = 4.772001873 Simplifying x2 = 4.772001873 Take the square root of each side: x = {-2.184491216, 2.184491216}Subproblem 2
x2 + -0.5 = -4.272001873 Simplifying x2 + -0.5 = -4.272001873 Reorder the terms: -0.5 + x2 = -4.272001873 Solving -0.5 + x2 = -4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x2 = -4.272001873 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = -4.272001873 + 0.5 x2 = -4.272001873 + 0.5 Combine like terms: -4.272001873 + 0.5 = -3.772001873 x2 = -3.772001873 Simplifying x2 = -3.772001873 Reorder the terms: 3.772001873 + x2 = -3.772001873 + 3.772001873 Combine like terms: -3.772001873 + 3.772001873 = 0.000000000 3.772001873 + 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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