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Simplifying 3a(-3a2 + 2a + -7) = 0 Reorder the terms: 3a(-7 + 2a + -3a2) = 0 (-7 * 3a + 2a * 3a + -3a2 * 3a) = 0 (-21a + 6a2 + -9a3) = 0 Solving -21a + 6a2 + -9a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3a'. 3a(-7 + 2a + -3a2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(-7 + 2a + -3a2)' equal to zero and attempt to solve: Simplifying -7 + 2a + -3a2 = 0 Solving -7 + 2a + -3a2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 2.333333333 + -0.6666666667a + a2 = 0 Move the constant term to the right: Add '-2.333333333' to each side of the equation. 2.333333333 + -0.6666666667a + -2.333333333 + a2 = 0 + -2.333333333 Reorder the terms: 2.333333333 + -2.333333333 + -0.6666666667a + a2 = 0 + -2.333333333 Combine like terms: 2.333333333 + -2.333333333 = 0.000000000 0.000000000 + -0.6666666667a + a2 = 0 + -2.333333333 -0.6666666667a + a2 = 0 + -2.333333333 Combine like terms: 0 + -2.333333333 = -2.333333333 -0.6666666667a + a2 = -2.333333333 The a term is -0.6666666667a. 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. -0.6666666667a + 0.1111111112 + a2 = -2.333333333 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667a + a2 = -2.333333333 + 0.1111111112 Combine like terms: -2.333333333 + 0.1111111112 = -2.2222222218 0.1111111112 + -0.6666666667a + a2 = -2.2222222218 Factor a perfect square on the left side: (a + -0.3333333334)(a + -0.3333333334) = -2.2222222218 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.Solution
a = {0}
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