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Simplifying 2a5b + 2a4b2 + 2a3b3 = 0 Reorder the terms: 2a3b3 + 2a4b2 + 2a5b = 0 Solving 2a3b3 + 2a4b2 + 2a5b = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2a3b'. 2a3b(b2 + ab + a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'a3b' equal to zero and attempt to solve: Simplifying a3b = 0 Solving a3b = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a3b = 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 '(b2 + ab + a2)' equal to zero and attempt to solve: Simplifying b2 + ab + a2 = 0 Reorder the terms: ab + a2 + b2 = 0 Solving ab + a2 + b2 = 0 Begin completing the square. Move the constant term to the right: Add '-1b2' to each side of the equation. ab + a2 + b2 + -1b2 = 0 + -1b2 Combine like terms: b2 + -1b2 = 0 ab + a2 + 0 = 0 + -1b2 ab + a2 = 0 + -1b2 Remove the zero: ab + a2 = -1b2 The a term is ab. Take half its coefficient (0.5b). Square it (0.25b2) and add it to both sides. Add '0.25b2' to each side of the equation. ab + a2 + 0.25b2 = -1b2 + 0.25b2 Combine like terms: -1b2 + 0.25b2 = -0.75b2 ab + a2 + 0.25b2 = -0.75b2 Factor a perfect square on the left side: (a + 0.5b)(a + 0.5b) = -0.75b2 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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