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Simplifying 16a2b + 24ab + 16b = 0 Reorder the terms: 24ab + 16a2b + 16b = 0 Solving 24ab + 16a2b + 16b = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '8b'. 8b(3a + 2a2 + 2) = 0 Ignore the factor 8.Subproblem 1
Set the factor 'b' equal to zero and attempt to solve: Simplifying b = 0 Solving b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. b + -1b = 0 + -1b Remove the zero: 0 = -1b Simplifying 0 = -1b 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 + 2a2 + 2)' equal to zero and attempt to solve: Simplifying 3a + 2a2 + 2 = 0 Reorder the terms: 2 + 3a + 2a2 = 0 Solving 2 + 3a + 2a2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1 + 1.5a + a2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 1.5a + -1 + a2 = 0 + -1 Reorder the terms: 1 + -1 + 1.5a + a2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 1.5a + a2 = 0 + -1 1.5a + a2 = 0 + -1 Combine like terms: 0 + -1 = -1 1.5a + a2 = -1 The a term is 1.5a. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5a + 0.5625 + a2 = -1 + 0.5625 Reorder the terms: 0.5625 + 1.5a + a2 = -1 + 0.5625 Combine like terms: -1 + 0.5625 = -0.4375 0.5625 + 1.5a + a2 = -0.4375 Factor a perfect square on the left side: (a + 0.75)(a + 0.75) = -0.4375 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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