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Simplifying (3x + -2)(3) = 54x2 + -27x + 4 Reorder the terms: (-2 + 3x)(3) = 54x2 + -27x + 4 Reorder the terms for easier multiplication: 3(-2 + 3x) = 54x2 + -27x + 4 (-2 * 3 + 3x * 3) = 54x2 + -27x + 4 (-6 + 9x) = 54x2 + -27x + 4 Reorder the terms: -6 + 9x = 4 + -27x + 54x2 Solving -6 + 9x = 4 + -27x + 54x2 Solving for variable 'x'. Reorder the terms: -6 + -4 + 9x + 27x + -54x2 = 4 + -27x + 54x2 + -4 + 27x + -54x2 Combine like terms: -6 + -4 = -10 -10 + 9x + 27x + -54x2 = 4 + -27x + 54x2 + -4 + 27x + -54x2 Combine like terms: 9x + 27x = 36x -10 + 36x + -54x2 = 4 + -27x + 54x2 + -4 + 27x + -54x2 Reorder the terms: -10 + 36x + -54x2 = 4 + -4 + -27x + 27x + 54x2 + -54x2 Combine like terms: 4 + -4 = 0 -10 + 36x + -54x2 = 0 + -27x + 27x + 54x2 + -54x2 -10 + 36x + -54x2 = -27x + 27x + 54x2 + -54x2 Combine like terms: -27x + 27x = 0 -10 + 36x + -54x2 = 0 + 54x2 + -54x2 -10 + 36x + -54x2 = 54x2 + -54x2 Combine like terms: 54x2 + -54x2 = 0 -10 + 36x + -54x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 18x + -27x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + 18x + -27x2)' equal to zero and attempt to solve: Simplifying -5 + 18x + -27x2 = 0 Solving -5 + 18x + -27x2 = 0 Begin completing the square. Divide all terms by -27 the coefficient of the squared term: Divide each side by '-27'. 0.1851851852 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '-0.1851851852' to each side of the equation. 0.1851851852 + -0.6666666667x + -0.1851851852 + x2 = 0 + -0.1851851852 Reorder the terms: 0.1851851852 + -0.1851851852 + -0.6666666667x + x2 = 0 + -0.1851851852 Combine like terms: 0.1851851852 + -0.1851851852 = 0.0000000000 0.0000000000 + -0.6666666667x + x2 = 0 + -0.1851851852 -0.6666666667x + x2 = 0 + -0.1851851852 Combine like terms: 0 + -0.1851851852 = -0.1851851852 -0.6666666667x + x2 = -0.1851851852 The x term is -0.6666666667x. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667x + 0.1111111112 + x2 = -0.1851851852 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = -0.1851851852 + 0.1111111112 Combine like terms: -0.1851851852 + 0.1111111112 = -0.074074074 0.1111111112 + -0.6666666667x + x2 = -0.074074074 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = -0.074074074 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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