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Simplifying 2a2 + 8a + -33 = 0 Reorder the terms: -33 + 8a + 2a2 = 0 Solving -33 + 8a + 2a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -16.5 + 4a + a2 = 0 Move the constant term to the right: Add '16.5' to each side of the equation. -16.5 + 4a + 16.5 + a2 = 0 + 16.5 Reorder the terms: -16.5 + 16.5 + 4a + a2 = 0 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + 4a + a2 = 0 + 16.5 4a + a2 = 0 + 16.5 Combine like terms: 0 + 16.5 = 16.5 4a + a2 = 16.5 The a term is 4a. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4a + 4 + a2 = 16.5 + 4 Reorder the terms: 4 + 4a + a2 = 16.5 + 4 Combine like terms: 16.5 + 4 = 20.5 4 + 4a + a2 = 20.5 Factor a perfect square on the left side: (a + 2)(a + 2) = 20.5 Calculate the square root of the right side: 4.527692569 Break this problem into two subproblems by setting (a + 2) equal to 4.527692569 and -4.527692569.Subproblem 1
a + 2 = 4.527692569 Simplifying a + 2 = 4.527692569 Reorder the terms: 2 + a = 4.527692569 Solving 2 + a = 4.527692569 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + a = 4.527692569 + -2 Combine like terms: 2 + -2 = 0 0 + a = 4.527692569 + -2 a = 4.527692569 + -2 Combine like terms: 4.527692569 + -2 = 2.527692569 a = 2.527692569 Simplifying a = 2.527692569Subproblem 2
a + 2 = -4.527692569 Simplifying a + 2 = -4.527692569 Reorder the terms: 2 + a = -4.527692569 Solving 2 + a = -4.527692569 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + a = -4.527692569 + -2 Combine like terms: 2 + -2 = 0 0 + a = -4.527692569 + -2 a = -4.527692569 + -2 Combine like terms: -4.527692569 + -2 = -6.527692569 a = -6.527692569 Simplifying a = -6.527692569Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.527692569, -6.527692569}
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