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Simplifying 2x2 + -6x + 108 = 0 Reorder the terms: 108 + -6x + 2x2 = 0 Solving 108 + -6x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(54 + -3x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(54 + -3x + x2)' equal to zero and attempt to solve: Simplifying 54 + -3x + x2 = 0 Solving 54 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-54' to each side of the equation. 54 + -3x + -54 + x2 = 0 + -54 Reorder the terms: 54 + -54 + -3x + x2 = 0 + -54 Combine like terms: 54 + -54 = 0 0 + -3x + x2 = 0 + -54 -3x + x2 = 0 + -54 Combine like terms: 0 + -54 = -54 -3x + x2 = -54 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -54 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -54 + 2.25 Combine like terms: -54 + 2.25 = -51.75 2.25 + -3x + x2 = -51.75 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = -51.75 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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