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Simplifying 24x2 + 36x + 27 = 0 Reorder the terms: 27 + 36x + 24x2 = 0 Solving 27 + 36x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(9 + 12x + 8x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(9 + 12x + 8x2)' equal to zero and attempt to solve: Simplifying 9 + 12x + 8x2 = 0 Solving 9 + 12x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.125 + 1.5x + x2 = 0 Move the constant term to the right: Add '-1.125' to each side of the equation. 1.125 + 1.5x + -1.125 + x2 = 0 + -1.125 Reorder the terms: 1.125 + -1.125 + 1.5x + x2 = 0 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + 1.5x + x2 = 0 + -1.125 1.5x + x2 = 0 + -1.125 Combine like terms: 0 + -1.125 = -1.125 1.5x + x2 = -1.125 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = -1.125 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -1.125 + 0.5625 Combine like terms: -1.125 + 0.5625 = -0.5625 0.5625 + 1.5x + x2 = -0.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = -0.5625 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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