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Simplifying 2a(7a2 + -3a + 9) = 0 Reorder the terms: 2a(9 + -3a + 7a2) = 0 (9 * 2a + -3a * 2a + 7a2 * 2a) = 0 (18a + -6a2 + 14a3) = 0 Solving 18a + -6a2 + 14a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2a'. 2a(9 + -3a + 7a2) = 0 Ignore the factor 2.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 '(9 + -3a + 7a2)' equal to zero and attempt to solve: Simplifying 9 + -3a + 7a2 = 0 Solving 9 + -3a + 7a2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1.285714286 + -0.4285714286a + a2 = 0 Move the constant term to the right: Add '-1.285714286' to each side of the equation. 1.285714286 + -0.4285714286a + -1.285714286 + a2 = 0 + -1.285714286 Reorder the terms: 1.285714286 + -1.285714286 + -0.4285714286a + a2 = 0 + -1.285714286 Combine like terms: 1.285714286 + -1.285714286 = 0.000000000 0.000000000 + -0.4285714286a + a2 = 0 + -1.285714286 -0.4285714286a + a2 = 0 + -1.285714286 Combine like terms: 0 + -1.285714286 = -1.285714286 -0.4285714286a + a2 = -1.285714286 The a term is -0.4285714286a. Take half its coefficient (-0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. -0.4285714286a + 0.04591836735 + a2 = -1.285714286 + 0.04591836735 Reorder the terms: 0.04591836735 + -0.4285714286a + a2 = -1.285714286 + 0.04591836735 Combine like terms: -1.285714286 + 0.04591836735 = -1.23979591865 0.04591836735 + -0.4285714286a + a2 = -1.23979591865 Factor a perfect square on the left side: (a + -0.2142857143)(a + -0.2142857143) = -1.23979591865 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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