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Simplifying 36x2 = 12x + -24 Reorder the terms: 36x2 = -24 + 12x Solving 36x2 = -24 + 12x Solving for variable 'x'. Reorder the terms: 24 + -12x + 36x2 = -24 + 12x + 24 + -12x Reorder the terms: 24 + -12x + 36x2 = -24 + 24 + 12x + -12x Combine like terms: -24 + 24 = 0 24 + -12x + 36x2 = 0 + 12x + -12x 24 + -12x + 36x2 = 12x + -12x Combine like terms: 12x + -12x = 0 24 + -12x + 36x2 = 0 Factor out the Greatest Common Factor (GCF), '12'. 12(2 + -1x + 3x2) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(2 + -1x + 3x2)' equal to zero and attempt to solve: Simplifying 2 + -1x + 3x2 = 0 Solving 2 + -1x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.6666666667 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + -0.3333333333x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + -0.3333333333x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + -0.3333333333x + x2 = 0 + -0.6666666667 -0.3333333333x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 -0.3333333333x + x2 = -0.6666666667 The x term is -0.3333333333x. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333x + 0.02777777779 + x2 = -0.6666666667 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = -0.6666666667 + 0.02777777779 Combine like terms: -0.6666666667 + 0.02777777779 = -0.63888888891 0.02777777779 + -0.3333333333x + x2 = -0.63888888891 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = -0.63888888891 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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