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Simplifying (27 + -1x) + -1x2 = 81 Remove parenthesis around (27 + -1x) 27 + -1x + -1x2 = 81 Solving 27 + -1x + -1x2 = 81 Solving for variable 'x'. Reorder the terms: 27 + -81 + -1x + -1x2 = 81 + -81 Combine like terms: 27 + -81 = -54 -54 + -1x + -1x2 = 81 + -81 Combine like terms: 81 + -81 = 0 -54 + -1x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(54 + x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(54 + x + x2)' equal to zero and attempt to solve: Simplifying 54 + x + x2 = 0 Solving 54 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-54' to each side of the equation. 54 + x + -54 + x2 = 0 + -54 Reorder the terms: 54 + -54 + x + x2 = 0 + -54 Combine like terms: 54 + -54 = 0 0 + x + x2 = 0 + -54 x + x2 = 0 + -54 Combine like terms: 0 + -54 = -54 x + x2 = -54 The x term is x. 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. x + 0.25 + x2 = -54 + 0.25 Reorder the terms: 0.25 + x + x2 = -54 + 0.25 Combine like terms: -54 + 0.25 = -53.75 0.25 + x + x2 = -53.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -53.75 Can't calculate square root of the right side. 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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