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Simplifying 6x2 + 27x + 105 = 0 Reorder the terms: 105 + 27x + 6x2 = 0 Solving 105 + 27x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(35 + 9x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(35 + 9x + 2x2)' equal to zero and attempt to solve: Simplifying 35 + 9x + 2x2 = 0 Solving 35 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 17.5 + 4.5x + x2 = 0 Move the constant term to the right: Add '-17.5' to each side of the equation. 17.5 + 4.5x + -17.5 + x2 = 0 + -17.5 Reorder the terms: 17.5 + -17.5 + 4.5x + x2 = 0 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + 4.5x + x2 = 0 + -17.5 4.5x + x2 = 0 + -17.5 Combine like terms: 0 + -17.5 = -17.5 4.5x + x2 = -17.5 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 = -17.5 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = -17.5 + 5.0625 Combine like terms: -17.5 + 5.0625 = -12.4375 5.0625 + 4.5x + x2 = -12.4375 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = -12.4375 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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