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Simplifying 3a2b + -4ab + 5b = 0 Reorder the terms: -4ab + 3a2b + 5b = 0 Solving -4ab + 3a2b + 5b = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'b'. b(-4a + 3a2 + 5) = 0Subproblem 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 '(-4a + 3a2 + 5)' equal to zero and attempt to solve: Simplifying -4a + 3a2 + 5 = 0 Reorder the terms: 5 + -4a + 3a2 = 0 Solving 5 + -4a + 3a2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.666666667 + -1.333333333a + a2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + -1.333333333a + -1.666666667 + a2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + -1.333333333a + a2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + -1.333333333a + a2 = 0 + -1.666666667 -1.333333333a + a2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 -1.333333333a + a2 = -1.666666667 The a term is -1.333333333a. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333a + 0.4444444442 + a2 = -1.666666667 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333a + a2 = -1.666666667 + 0.4444444442 Combine like terms: -1.666666667 + 0.4444444442 = -1.2222222228 0.4444444442 + -1.333333333a + a2 = -1.2222222228 Factor a perfect square on the left side: (a + -0.6666666665)(a + -0.6666666665) = -1.2222222228 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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