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Simplifying 3a2(2a2 + -7a + -8) = 0 Reorder the terms: 3a2(-8 + -7a + 2a2) = 0 (-8 * 3a2 + -7a * 3a2 + 2a2 * 3a2) = 0 (-24a2 + -21a3 + 6a4) = 0 Solving -24a2 + -21a3 + 6a4 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3a2'. 3a2(-8 + -7a + 2a2) = 0 Ignore the factor 3.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 '(-8 + -7a + 2a2)' equal to zero and attempt to solve: Simplifying -8 + -7a + 2a2 = 0 Solving -8 + -7a + 2a2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4 + -3.5a + a2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -3.5a + 4 + a2 = 0 + 4 Reorder the terms: -4 + 4 + -3.5a + a2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3.5a + a2 = 0 + 4 -3.5a + a2 = 0 + 4 Combine like terms: 0 + 4 = 4 -3.5a + a2 = 4 The a term is -3.5a. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5a + 3.0625 + a2 = 4 + 3.0625 Reorder the terms: 3.0625 + -3.5a + a2 = 4 + 3.0625 Combine like terms: 4 + 3.0625 = 7.0625 3.0625 + -3.5a + a2 = 7.0625 Factor a perfect square on the left side: (a + -1.75)(a + -1.75) = 7.0625 Calculate the square root of the right side: 2.657536453 Break this problem into two subproblems by setting (a + -1.75) equal to 2.657536453 and -2.657536453.Subproblem 1
a + -1.75 = 2.657536453 Simplifying a + -1.75 = 2.657536453 Reorder the terms: -1.75 + a = 2.657536453 Solving -1.75 + a = 2.657536453 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + a = 2.657536453 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + a = 2.657536453 + 1.75 a = 2.657536453 + 1.75 Combine like terms: 2.657536453 + 1.75 = 4.407536453 a = 4.407536453 Simplifying a = 4.407536453Subproblem 2
a + -1.75 = -2.657536453 Simplifying a + -1.75 = -2.657536453 Reorder the terms: -1.75 + a = -2.657536453 Solving -1.75 + a = -2.657536453 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + a = -2.657536453 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + a = -2.657536453 + 1.75 a = -2.657536453 + 1.75 Combine like terms: -2.657536453 + 1.75 = -0.907536453 a = -0.907536453 Simplifying a = -0.907536453Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.407536453, -0.907536453}Solution
a = {0, 4.407536453, -0.907536453}
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