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Simplifying 2a3 + 9a2 + -9a = 0 Reorder the terms: -9a + 9a2 + 2a3 = 0 Solving -9a + 9a2 + 2a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a'. a(-9 + 9a + 2a2) = 0Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(-9 + 9a + 2a2)' equal to zero and attempt to solve: Simplifying -9 + 9a + 2a2 = 0 Solving -9 + 9a + 2a2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4.5 + 4.5a + a2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 4.5a + 4.5 + a2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + 4.5a + a2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 4.5a + a2 = 0 + 4.5 4.5a + a2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 4.5a + a2 = 4.5 The a term is 4.5a. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5a + 5.0625 + a2 = 4.5 + 5.0625 Reorder the terms: 5.0625 + 4.5a + a2 = 4.5 + 5.0625 Combine like terms: 4.5 + 5.0625 = 9.5625 5.0625 + 4.5a + a2 = 9.5625 Factor a perfect square on the left side: (a + 2.25)(a + 2.25) = 9.5625 Calculate the square root of the right side: 3.092329219 Break this problem into two subproblems by setting (a + 2.25) equal to 3.092329219 and -3.092329219.Subproblem 1
a + 2.25 = 3.092329219 Simplifying a + 2.25 = 3.092329219 Reorder the terms: 2.25 + a = 3.092329219 Solving 2.25 + a = 3.092329219 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + a = 3.092329219 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + a = 3.092329219 + -2.25 a = 3.092329219 + -2.25 Combine like terms: 3.092329219 + -2.25 = 0.842329219 a = 0.842329219 Simplifying a = 0.842329219Subproblem 2
a + 2.25 = -3.092329219 Simplifying a + 2.25 = -3.092329219 Reorder the terms: 2.25 + a = -3.092329219 Solving 2.25 + a = -3.092329219 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + a = -3.092329219 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + a = -3.092329219 + -2.25 a = -3.092329219 + -2.25 Combine like terms: -3.092329219 + -2.25 = -5.342329219 a = -5.342329219 Simplifying a = -5.342329219Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.842329219, -5.342329219}Solution
a = {0, 0.842329219, -5.342329219}
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