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Simplifying 6x2 + -27x + 60 = 0 Reorder the terms: 60 + -27x + 6x2 = 0 Solving 60 + -27x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(20 + -9x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(20 + -9x + 2x2)' equal to zero and attempt to solve: Simplifying 20 + -9x + 2x2 = 0 Solving 20 + -9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 10 + -4.5x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -4.5x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -4.5x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -4.5x + x2 = 0 + -10 -4.5x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -4.5x + x2 = -10 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 = -10 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = -10 + 5.0625 Combine like terms: -10 + 5.0625 = -4.9375 5.0625 + -4.5x + x2 = -4.9375 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = -4.9375 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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