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Simplifying 3a2b2 + -9ab2 + 15b2 = 0 Reorder the terms: -9ab2 + 3a2b2 + 15b2 = 0 Solving -9ab2 + 3a2b2 + 15b2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3b2'. 3b2(-3a + a2 + 5) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'b2' equal to zero and attempt to solve: Simplifying b2 = 0 Solving b2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b2' to each side of the equation. b2 + -1b2 = 0 + -1b2 Remove the zero: 0 = -1b2 Simplifying 0 = -1b2 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 '(-3a + a2 + 5)' equal to zero and attempt to solve: Simplifying -3a + a2 + 5 = 0 Reorder the terms: 5 + -3a + a2 = 0 Solving 5 + -3a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -3a + -5 + a2 = 0 + -5 Reorder the terms: 5 + -5 + -3a + a2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3a + a2 = 0 + -5 -3a + a2 = 0 + -5 Combine like terms: 0 + -5 = -5 -3a + a2 = -5 The a term is -3a. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3a + 2.25 + a2 = -5 + 2.25 Reorder the terms: 2.25 + -3a + a2 = -5 + 2.25 Combine like terms: -5 + 2.25 = -2.75 2.25 + -3a + a2 = -2.75 Factor a perfect square on the left side: (a + -1.5)(a + -1.5) = -2.75 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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