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Simplifying 27x2 + 24x + 144 = 0 Reorder the terms: 144 + 24x + 27x2 = 0 Solving 144 + 24x + 27x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(48 + 8x + 9x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(48 + 8x + 9x2)' equal to zero and attempt to solve: Simplifying 48 + 8x + 9x2 = 0 Solving 48 + 8x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 5.333333333 + 0.8888888889x + x2 = 0 Move the constant term to the right: Add '-5.333333333' to each side of the equation. 5.333333333 + 0.8888888889x + -5.333333333 + x2 = 0 + -5.333333333 Reorder the terms: 5.333333333 + -5.333333333 + 0.8888888889x + x2 = 0 + -5.333333333 Combine like terms: 5.333333333 + -5.333333333 = 0.000000000 0.000000000 + 0.8888888889x + x2 = 0 + -5.333333333 0.8888888889x + x2 = 0 + -5.333333333 Combine like terms: 0 + -5.333333333 = -5.333333333 0.8888888889x + x2 = -5.333333333 The x term is 0.8888888889x. Take half its coefficient (0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. 0.8888888889x + 0.1975308642 + x2 = -5.333333333 + 0.1975308642 Reorder the terms: 0.1975308642 + 0.8888888889x + x2 = -5.333333333 + 0.1975308642 Combine like terms: -5.333333333 + 0.1975308642 = -5.1358024688 0.1975308642 + 0.8888888889x + x2 = -5.1358024688 Factor a perfect square on the left side: (x + 0.4444444445)(x + 0.4444444445) = -5.1358024688 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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