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Simplifying 2a(5a2 + 3a + -17) = 0 Reorder the terms: 2a(-17 + 3a + 5a2) = 0 (-17 * 2a + 3a * 2a + 5a2 * 2a) = 0 (-34a + 6a2 + 10a3) = 0 Solving -34a + 6a2 + 10a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2a'. 2a(-17 + 3a + 5a2) = 0 Ignore the factor 2.Subproblem 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 '(-17 + 3a + 5a2)' equal to zero and attempt to solve: Simplifying -17 + 3a + 5a2 = 0 Solving -17 + 3a + 5a2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.4 + 0.6a + a2 = 0 Move the constant term to the right: Add '3.4' to each side of the equation. -3.4 + 0.6a + 3.4 + a2 = 0 + 3.4 Reorder the terms: -3.4 + 3.4 + 0.6a + a2 = 0 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + 0.6a + a2 = 0 + 3.4 0.6a + a2 = 0 + 3.4 Combine like terms: 0 + 3.4 = 3.4 0.6a + a2 = 3.4 The a term is 0.6a. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6a + 0.09 + a2 = 3.4 + 0.09 Reorder the terms: 0.09 + 0.6a + a2 = 3.4 + 0.09 Combine like terms: 3.4 + 0.09 = 3.49 0.09 + 0.6a + a2 = 3.49 Factor a perfect square on the left side: (a + 0.3)(a + 0.3) = 3.49 Calculate the square root of the right side: 1.868154169 Break this problem into two subproblems by setting (a + 0.3) equal to 1.868154169 and -1.868154169.Subproblem 1
a + 0.3 = 1.868154169 Simplifying a + 0.3 = 1.868154169 Reorder the terms: 0.3 + a = 1.868154169 Solving 0.3 + a = 1.868154169 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + a = 1.868154169 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + a = 1.868154169 + -0.3 a = 1.868154169 + -0.3 Combine like terms: 1.868154169 + -0.3 = 1.568154169 a = 1.568154169 Simplifying a = 1.568154169Subproblem 2
a + 0.3 = -1.868154169 Simplifying a + 0.3 = -1.868154169 Reorder the terms: 0.3 + a = -1.868154169 Solving 0.3 + a = -1.868154169 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + a = -1.868154169 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + a = -1.868154169 + -0.3 a = -1.868154169 + -0.3 Combine like terms: -1.868154169 + -0.3 = -2.168154169 a = -2.168154169 Simplifying a = -2.168154169Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.568154169, -2.168154169}Solution
a = {0, 1.568154169, -2.168154169}
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