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Simplifying 27x2 + -12x + 18 = 0 Reorder the terms: 18 + -12x + 27x2 = 0 Solving 18 + -12x + 27x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(6 + -4x + 9x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(6 + -4x + 9x2)' equal to zero and attempt to solve: Simplifying 6 + -4x + 9x2 = 0 Solving 6 + -4x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.6666666667 + -0.4444444444x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + -0.4444444444x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + -0.4444444444x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + -0.4444444444x + x2 = 0 + -0.6666666667 -0.4444444444x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 -0.4444444444x + x2 = -0.6666666667 The x term is -0.4444444444x. Take half its coefficient (-0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. -0.4444444444x + 0.04938271604 + x2 = -0.6666666667 + 0.04938271604 Reorder the terms: 0.04938271604 + -0.4444444444x + x2 = -0.6666666667 + 0.04938271604 Combine like terms: -0.6666666667 + 0.04938271604 = -0.61728395066 0.04938271604 + -0.4444444444x + x2 = -0.61728395066 Factor a perfect square on the left side: (x + -0.2222222222)(x + -0.2222222222) = -0.61728395066 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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