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Simplifying -3a10 + 9a5 + 6a15 = 0 Reorder the terms: 9a5 + -3a10 + 6a15 = 0 Solving 9a5 + -3a10 + 6a15 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3a5'. 3a5(3 + -1a5 + 2a10) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'a5' equal to zero and attempt to solve: Simplifying a5 = 0 Solving a5 = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a5 = 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 '(3 + -1a5 + 2a10)' equal to zero and attempt to solve: Simplifying 3 + -1a5 + 2a10 = 0 Solving 3 + -1a5 + 2a10 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + -0.5a5 + a10 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -0.5a5 + -1.5 + a10 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -0.5a5 + a10 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -0.5a5 + a10 = 0 + -1.5 -0.5a5 + a10 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -0.5a5 + a10 = -1.5 The a term is -0.5a5. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5a5 + 0.0625 + a10 = -1.5 + 0.0625 Reorder the terms: 0.0625 + -0.5a5 + a10 = -1.5 + 0.0625 Combine like terms: -1.5 + 0.0625 = -1.4375 0.0625 + -0.5a5 + a10 = -1.4375 Factor a perfect square on the left side: (a5 + -0.25)(a5 + -0.25) = -1.4375 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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