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Simplifying x6 + -1x3 = 27 Reorder the terms: -1x3 + x6 = 27 Solving -1x3 + x6 = 27 Solving for variable 'x'. Reorder the terms: -27 + -1x3 + x6 = 27 + -27 Combine like terms: 27 + -27 = 0 -27 + -1x3 + x6 = 0 Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + -1x3 + 27 + x6 = 0 + 27 Reorder the terms: -27 + 27 + -1x3 + x6 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -1x3 + x6 = 0 + 27 -1x3 + x6 = 0 + 27 Combine like terms: 0 + 27 = 27 -1x3 + x6 = 27 The x term is -1x3. 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. -1x3 + 0.25 + x6 = 27 + 0.25 Reorder the terms: 0.25 + -1x3 + x6 = 27 + 0.25 Combine like terms: 27 + 0.25 = 27.25 0.25 + -1x3 + x6 = 27.25 Factor a perfect square on the left side: (x3 + -0.5)(x3 + -0.5) = 27.25 Calculate the square root of the right side: 5.220153254 Break this problem into two subproblems by setting (x3 + -0.5) equal to 5.220153254 and -5.220153254.Subproblem 1
x3 + -0.5 = 5.220153254 Simplifying x3 + -0.5 = 5.220153254 Reorder the terms: -0.5 + x3 = 5.220153254 Solving -0.5 + x3 = 5.220153254 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 + x3 = 5.220153254 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x3 = 5.220153254 + 0.5 x3 = 5.220153254 + 0.5 Combine like terms: 5.220153254 + 0.5 = 5.720153254 x3 = 5.720153254 Simplifying x3 = 5.720153254 Reorder the terms: -5.720153254 + x3 = 5.720153254 + -5.720153254 Combine like terms: 5.720153254 + -5.720153254 = 0.000000000 -5.720153254 + x3 = 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
x3 + -0.5 = -5.220153254 Simplifying x3 + -0.5 = -5.220153254 Reorder the terms: -0.5 + x3 = -5.220153254 Solving -0.5 + x3 = -5.220153254 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 + x3 = -5.220153254 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x3 = -5.220153254 + 0.5 x3 = -5.220153254 + 0.5 Combine like terms: -5.220153254 + 0.5 = -4.720153254 x3 = -4.720153254 Simplifying x3 = -4.720153254 Reorder the terms: 4.720153254 + x3 = -4.720153254 + 4.720153254 Combine like terms: -4.720153254 + 4.720153254 = 0.000000000 4.720153254 + x3 = 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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