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Simplifying 27x + -6x2 = 132 Solving 27x + -6x2 = 132 Solving for variable 'x'. Reorder the terms: -132 + 27x + -6x2 = 132 + -132 Combine like terms: 132 + -132 = 0 -132 + 27x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-44 + 9x + -2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-44 + 9x + -2x2)' equal to zero and attempt to solve: Simplifying -44 + 9x + -2x2 = 0 Solving -44 + 9x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 22 + -4.5x + x2 = 0 Move the constant term to the right: Add '-22' to each side of the equation. 22 + -4.5x + -22 + x2 = 0 + -22 Reorder the terms: 22 + -22 + -4.5x + x2 = 0 + -22 Combine like terms: 22 + -22 = 0 0 + -4.5x + x2 = 0 + -22 -4.5x + x2 = 0 + -22 Combine like terms: 0 + -22 = -22 -4.5x + x2 = -22 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = -22 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = -22 + 5.0625 Combine like terms: -22 + 5.0625 = -16.9375 5.0625 + -4.5x + x2 = -16.9375 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = -16.9375 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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