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Simplifying 2a2(3a2 + 4a + -3) = 0 Reorder the terms: 2a2(-3 + 4a + 3a2) = 0 (-3 * 2a2 + 4a * 2a2 + 3a2 * 2a2) = 0 (-6a2 + 8a3 + 6a4) = 0 Solving -6a2 + 8a3 + 6a4 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2a2'. 2a2(-3 + 4a + 3a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'a2' equal to zero and attempt to solve: Simplifying a2 = 0 Solving a2 = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a2 = 0 Take the square root of each side: a = {0}Subproblem 2
Set the factor '(-3 + 4a + 3a2)' equal to zero and attempt to solve: Simplifying -3 + 4a + 3a2 = 0 Solving -3 + 4a + 3a2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1 + 1.333333333a + a2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 1.333333333a + 1 + a2 = 0 + 1 Reorder the terms: -1 + 1 + 1.333333333a + a2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 1.333333333a + a2 = 0 + 1 1.333333333a + a2 = 0 + 1 Combine like terms: 0 + 1 = 1 1.333333333a + a2 = 1 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 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333a + a2 = 1 + 0.4444444442 Combine like terms: 1 + 0.4444444442 = 1.4444444442 0.4444444442 + 1.333333333a + a2 = 1.4444444442 Factor a perfect square on the left side: (a + 0.6666666665)(a + 0.6666666665) = 1.4444444442 Calculate the square root of the right side: 1.201850425 Break this problem into two subproblems by setting (a + 0.6666666665) equal to 1.201850425 and -1.201850425.Subproblem 1
a + 0.6666666665 = 1.201850425 Simplifying a + 0.6666666665 = 1.201850425 Reorder the terms: 0.6666666665 + a = 1.201850425 Solving 0.6666666665 + a = 1.201850425 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + a = 1.201850425 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + a = 1.201850425 + -0.6666666665 a = 1.201850425 + -0.6666666665 Combine like terms: 1.201850425 + -0.6666666665 = 0.5351837585 a = 0.5351837585 Simplifying a = 0.5351837585Subproblem 2
a + 0.6666666665 = -1.201850425 Simplifying a + 0.6666666665 = -1.201850425 Reorder the terms: 0.6666666665 + a = -1.201850425 Solving 0.6666666665 + a = -1.201850425 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + a = -1.201850425 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + a = -1.201850425 + -0.6666666665 a = -1.201850425 + -0.6666666665 Combine like terms: -1.201850425 + -0.6666666665 = -1.8685170915 a = -1.8685170915 Simplifying a = -1.8685170915Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.5351837585, -1.8685170915}Solution
a = {0, 0.5351837585, -1.8685170915}
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