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Simplifying 4a2 + -11a + -35 = 0 Reorder the terms: -35 + -11a + 4a2 = 0 Solving -35 + -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'. -8.75 + -2.75a + a2 = 0 Move the constant term to the right: Add '8.75' to each side of the equation. -8.75 + -2.75a + 8.75 + a2 = 0 + 8.75 Reorder the terms: -8.75 + 8.75 + -2.75a + a2 = 0 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + -2.75a + a2 = 0 + 8.75 -2.75a + a2 = 0 + 8.75 Combine like terms: 0 + 8.75 = 8.75 -2.75a + a2 = 8.75 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 = 8.75 + 1.890625 Reorder the terms: 1.890625 + -2.75a + a2 = 8.75 + 1.890625 Combine like terms: 8.75 + 1.890625 = 10.640625 1.890625 + -2.75a + a2 = 10.640625 Factor a perfect square on the left side: (a + -1.375)(a + -1.375) = 10.640625 Calculate the square root of the right side: 3.261997088 Break this problem into two subproblems by setting (a + -1.375) equal to 3.261997088 and -3.261997088.Subproblem 1
a + -1.375 = 3.261997088 Simplifying a + -1.375 = 3.261997088 Reorder the terms: -1.375 + a = 3.261997088 Solving -1.375 + a = 3.261997088 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 = 3.261997088 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + a = 3.261997088 + 1.375 a = 3.261997088 + 1.375 Combine like terms: 3.261997088 + 1.375 = 4.636997088 a = 4.636997088 Simplifying a = 4.636997088Subproblem 2
a + -1.375 = -3.261997088 Simplifying a + -1.375 = -3.261997088 Reorder the terms: -1.375 + a = -3.261997088 Solving -1.375 + a = -3.261997088 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 = -3.261997088 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + a = -3.261997088 + 1.375 a = -3.261997088 + 1.375 Combine like terms: -3.261997088 + 1.375 = -1.886997088 a = -1.886997088 Simplifying a = -1.886997088Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.636997088, -1.886997088}
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