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Simplifying 18x = 6x2 + 27 Reorder the terms: 18x = 27 + 6x2 Solving 18x = 27 + 6x2 Solving for variable 'x'. Reorder the terms: -27 + 18x + -6x2 = 27 + 6x2 + -27 + -6x2 Reorder the terms: -27 + 18x + -6x2 = 27 + -27 + 6x2 + -6x2 Combine like terms: 27 + -27 = 0 -27 + 18x + -6x2 = 0 + 6x2 + -6x2 -27 + 18x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -27 + 18x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-9 + 6x + -2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-9 + 6x + -2x2)' equal to zero and attempt to solve: Simplifying -9 + 6x + -2x2 = 0 Solving -9 + 6x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 4.5 + -3x + x2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + -3x + -4.5 + x2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + -3x + x2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + -3x + x2 = 0 + -4.5 -3x + x2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 -3x + x2 = -4.5 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 = -4.5 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -4.5 + 2.25 Combine like terms: -4.5 + 2.25 = -2.25 2.25 + -3x + x2 = -2.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = -2.25 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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