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Simplifying 4a2 + -11a + -4 = 0 Reorder the terms: -4 + -11a + 4a2 = 0 Solving -4 + -11a + 4a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1 + -2.75a + a2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -2.75a + 1 + a2 = 0 + 1 Reorder the terms: -1 + 1 + -2.75a + a2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2.75a + a2 = 0 + 1 -2.75a + a2 = 0 + 1 Combine like terms: 0 + 1 = 1 -2.75a + a2 = 1 The a term is -2.75a. Take half its coefficient (-1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. -2.75a + 1.890625 + a2 = 1 + 1.890625 Reorder the terms: 1.890625 + -2.75a + a2 = 1 + 1.890625 Combine like terms: 1 + 1.890625 = 2.890625 1.890625 + -2.75a + a2 = 2.890625 Factor a perfect square on the left side: (a + -1.375)(a + -1.375) = 2.890625 Calculate the square root of the right side: 1.700183814 Break this problem into two subproblems by setting (a + -1.375) equal to 1.700183814 and -1.700183814.Subproblem 1
a + -1.375 = 1.700183814 Simplifying a + -1.375 = 1.700183814 Reorder the terms: -1.375 + a = 1.700183814 Solving -1.375 + a = 1.700183814 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + a = 1.700183814 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + a = 1.700183814 + 1.375 a = 1.700183814 + 1.375 Combine like terms: 1.700183814 + 1.375 = 3.075183814 a = 3.075183814 Simplifying a = 3.075183814Subproblem 2
a + -1.375 = -1.700183814 Simplifying a + -1.375 = -1.700183814 Reorder the terms: -1.375 + a = -1.700183814 Solving -1.375 + a = -1.700183814 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + a = -1.700183814 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + a = -1.700183814 + 1.375 a = -1.700183814 + 1.375 Combine like terms: -1.700183814 + 1.375 = -0.325183814 a = -0.325183814 Simplifying a = -0.325183814Solution
The solution to the problem is based on the solutions from the subproblems. a = {3.075183814, -0.325183814}
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