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Simplifying 14a4 + 21a6 + 12a5 = 0 Reorder the terms: 14a4 + 12a5 + 21a6 = 0 Solving 14a4 + 12a5 + 21a6 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a4'. a4(14 + 12a + 21a2) = 0Subproblem 1
Set the factor 'a4' equal to zero and attempt to solve: Simplifying a4 = 0 Solving a4 = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a4 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(14 + 12a + 21a2)' equal to zero and attempt to solve: Simplifying 14 + 12a + 21a2 = 0 Solving 14 + 12a + 21a2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. 0.6666666667 + 0.5714285714a + a2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + 0.5714285714a + -0.6666666667 + a2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + 0.5714285714a + a2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + 0.5714285714a + a2 = 0 + -0.6666666667 0.5714285714a + a2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 0.5714285714a + a2 = -0.6666666667 The a term is 0.5714285714a. Take half its coefficient (0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. 0.5714285714a + 0.08163265305 + a2 = -0.6666666667 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714a + a2 = -0.6666666667 + 0.08163265305 Combine like terms: -0.6666666667 + 0.08163265305 = -0.58503401365 0.08163265305 + 0.5714285714a + a2 = -0.58503401365 Factor a perfect square on the left side: (a + 0.2857142857)(a + 0.2857142857) = -0.58503401365 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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