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Simplifying 27x2 + 6x + 60 = 0 Reorder the terms: 60 + 6x + 27x2 = 0 Solving 60 + 6x + 27x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(20 + 2x + 9x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(20 + 2x + 9x2)' equal to zero and attempt to solve: Simplifying 20 + 2x + 9x2 = 0 Solving 20 + 2x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 2.222222222 + 0.2222222222x + x2 = 0 Move the constant term to the right: Add '-2.222222222' to each side of the equation. 2.222222222 + 0.2222222222x + -2.222222222 + x2 = 0 + -2.222222222 Reorder the terms: 2.222222222 + -2.222222222 + 0.2222222222x + x2 = 0 + -2.222222222 Combine like terms: 2.222222222 + -2.222222222 = 0.000000000 0.000000000 + 0.2222222222x + x2 = 0 + -2.222222222 0.2222222222x + x2 = 0 + -2.222222222 Combine like terms: 0 + -2.222222222 = -2.222222222 0.2222222222x + x2 = -2.222222222 The x term is 0.2222222222x. Take half its coefficient (0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. 0.2222222222x + 0.01234567901 + x2 = -2.222222222 + 0.01234567901 Reorder the terms: 0.01234567901 + 0.2222222222x + x2 = -2.222222222 + 0.01234567901 Combine like terms: -2.222222222 + 0.01234567901 = -2.20987654299 0.01234567901 + 0.2222222222x + x2 = -2.20987654299 Factor a perfect square on the left side: (x + 0.1111111111)(x + 0.1111111111) = -2.20987654299 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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