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Simplifying -2a2(9 + -1a + -4a2) = 0 (9 * -2a2 + -1a * -2a2 + -4a2 * -2a2) = 0 (-18a2 + 2a3 + 8a4) = 0 Solving -18a2 + 2a3 + 8a4 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2a2'. 2a2(-9 + a + 4a2) = 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 '(-9 + a + 4a2)' equal to zero and attempt to solve: Simplifying -9 + a + 4a2 = 0 Solving -9 + a + 4a2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.25 + 0.25a + a2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + 0.25a + 2.25 + a2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + 0.25a + a2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + 0.25a + a2 = 0 + 2.25 0.25a + a2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 0.25a + a2 = 2.25 The a term is a. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.25a + 0.25 + a2 = 2.25 + 0.25 Reorder the terms: 0.25 + 0.25a + a2 = 2.25 + 0.25 Combine like terms: 2.25 + 0.25 = 2.5 0.25 + 0.25a + a2 = 2.5 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = 2.5 Calculate the square root of the right side: 1.58113883 Break this problem into two subproblems by setting (a + 0.5) equal to 1.58113883 and -1.58113883.Subproblem 1
a + 0.5 = 1.58113883 Simplifying a + 0.5 = 1.58113883 Reorder the terms: 0.5 + a = 1.58113883 Solving 0.5 + a = 1.58113883 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = 1.58113883 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = 1.58113883 + -0.5 a = 1.58113883 + -0.5 Combine like terms: 1.58113883 + -0.5 = 1.08113883 a = 1.08113883 Simplifying a = 1.08113883Subproblem 2
a + 0.5 = -1.58113883 Simplifying a + 0.5 = -1.58113883 Reorder the terms: 0.5 + a = -1.58113883 Solving 0.5 + a = -1.58113883 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = -1.58113883 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = -1.58113883 + -0.5 a = -1.58113883 + -0.5 Combine like terms: -1.58113883 + -0.5 = -2.08113883 a = -2.08113883 Simplifying a = -2.08113883Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.08113883, -2.08113883}Solution
a = {0, 1.08113883, -2.08113883}
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