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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 + -1a + -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 + -1a + -4a2)' equal to zero and attempt to solve: Simplifying 9 + -1a + -4a2 = 0 Solving 9 + -1a + -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 0.25a. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25a + 0.015625 + a2 = 2.25 + 0.015625 Reorder the terms: 0.015625 + 0.25a + a2 = 2.25 + 0.015625 Combine like terms: 2.25 + 0.015625 = 2.265625 0.015625 + 0.25a + a2 = 2.265625 Factor a perfect square on the left side: (a + 0.125)(a + 0.125) = 2.265625 Calculate the square root of the right side: 1.505199322 Break this problem into two subproblems by setting (a + 0.125) equal to 1.505199322 and -1.505199322.Subproblem 1
a + 0.125 = 1.505199322 Simplifying a + 0.125 = 1.505199322 Reorder the terms: 0.125 + a = 1.505199322 Solving 0.125 + a = 1.505199322 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + a = 1.505199322 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + a = 1.505199322 + -0.125 a = 1.505199322 + -0.125 Combine like terms: 1.505199322 + -0.125 = 1.380199322 a = 1.380199322 Simplifying a = 1.380199322Subproblem 2
a + 0.125 = -1.505199322 Simplifying a + 0.125 = -1.505199322 Reorder the terms: 0.125 + a = -1.505199322 Solving 0.125 + a = -1.505199322 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + a = -1.505199322 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + a = -1.505199322 + -0.125 a = -1.505199322 + -0.125 Combine like terms: -1.505199322 + -0.125 = -1.630199322 a = -1.630199322 Simplifying a = -1.630199322Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.380199322, -1.630199322}Solution
a = {0, 1.380199322, -1.630199322}
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