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Simplifying 2a2(6a2 + -8a + -3) = 0 Reorder the terms: 2a2(-3 + -8a + 6a2) = 0 (-3 * 2a2 + -8a * 2a2 + 6a2 * 2a2) = 0 (-6a2 + -16a3 + 12a4) = 0 Solving -6a2 + -16a3 + 12a4 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2a2'. 2a2(-3 + -8a + 6a2) = 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 + -8a + 6a2)' equal to zero and attempt to solve: Simplifying -3 + -8a + 6a2 = 0 Solving -3 + -8a + 6a2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.5 + -1.333333333a + a2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -1.333333333a + 0.5 + a2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -1.333333333a + a2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -1.333333333a + a2 = 0 + 0.5 -1.333333333a + a2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -1.333333333a + a2 = 0.5 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 = 0.5 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333a + a2 = 0.5 + 0.4444444442 Combine like terms: 0.5 + 0.4444444442 = 0.9444444442 0.4444444442 + -1.333333333a + a2 = 0.9444444442 Factor a perfect square on the left side: (a + -0.6666666665)(a + -0.6666666665) = 0.9444444442 Calculate the square root of the right side: 0.971825316 Break this problem into two subproblems by setting (a + -0.6666666665) equal to 0.971825316 and -0.971825316.Subproblem 1
a + -0.6666666665 = 0.971825316 Simplifying a + -0.6666666665 = 0.971825316 Reorder the terms: -0.6666666665 + a = 0.971825316 Solving -0.6666666665 + a = 0.971825316 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 = 0.971825316 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + a = 0.971825316 + 0.6666666665 a = 0.971825316 + 0.6666666665 Combine like terms: 0.971825316 + 0.6666666665 = 1.6384919825 a = 1.6384919825 Simplifying a = 1.6384919825Subproblem 2
a + -0.6666666665 = -0.971825316 Simplifying a + -0.6666666665 = -0.971825316 Reorder the terms: -0.6666666665 + a = -0.971825316 Solving -0.6666666665 + a = -0.971825316 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 = -0.971825316 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + a = -0.971825316 + 0.6666666665 a = -0.971825316 + 0.6666666665 Combine like terms: -0.971825316 + 0.6666666665 = -0.3051586495 a = -0.3051586495 Simplifying a = -0.3051586495Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.6384919825, -0.3051586495}Solution
a = {0, 1.6384919825, -0.3051586495}
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