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Simplifying 27x2 + 72x + 1296 = 0 Reorder the terms: 1296 + 72x + 27x2 = 0 Solving 1296 + 72x + 27x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '9'. 9(144 + 8x + 3x2) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(144 + 8x + 3x2)' equal to zero and attempt to solve: Simplifying 144 + 8x + 3x2 = 0 Solving 144 + 8x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 48 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '-48' to each side of the equation. 48 + 2.666666667x + -48 + x2 = 0 + -48 Reorder the terms: 48 + -48 + 2.666666667x + x2 = 0 + -48 Combine like terms: 48 + -48 = 0 0 + 2.666666667x + x2 = 0 + -48 2.666666667x + x2 = 0 + -48 Combine like terms: 0 + -48 = -48 2.666666667x + x2 = -48 The x term is 2.666666667x. Take half its coefficient (1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. 2.666666667x + 1.777777780 + x2 = -48 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = -48 + 1.777777780 Combine like terms: -48 + 1.777777780 = -46.22222222 1.777777780 + 2.666666667x + x2 = -46.22222222 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = -46.22222222 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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