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Simplifying (3a + -4a2) + -1(-8a + -8) = 0 Remove parenthesis around (3a + -4a2) 3a + -4a2 + -1(-8a + -8) = 0 Reorder the terms: 3a + -4a2 + -1(-8 + -8a) = 0 3a + -4a2 + (-8 * -1 + -8a * -1) = 0 3a + -4a2 + (8 + 8a) = 0 Reorder the terms: 8 + 3a + 8a + -4a2 = 0 Combine like terms: 3a + 8a = 11a 8 + 11a + -4a2 = 0 Solving 8 + 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'. -2 + -2.75a + a2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -2.75a + 2 + a2 = 0 + 2 Reorder the terms: -2 + 2 + -2.75a + a2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -2.75a + a2 = 0 + 2 -2.75a + a2 = 0 + 2 Combine like terms: 0 + 2 = 2 -2.75a + a2 = 2 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 = 2 + 1.890625 Reorder the terms: 1.890625 + -2.75a + a2 = 2 + 1.890625 Combine like terms: 2 + 1.890625 = 3.890625 1.890625 + -2.75a + a2 = 3.890625 Factor a perfect square on the left side: (a + -1.375)(a + -1.375) = 3.890625 Calculate the square root of the right side: 1.97246673 Break this problem into two subproblems by setting (a + -1.375) equal to 1.97246673 and -1.97246673.Subproblem 1
a + -1.375 = 1.97246673 Simplifying a + -1.375 = 1.97246673 Reorder the terms: -1.375 + a = 1.97246673 Solving -1.375 + a = 1.97246673 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 = 1.97246673 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + a = 1.97246673 + 1.375 a = 1.97246673 + 1.375 Combine like terms: 1.97246673 + 1.375 = 3.34746673 a = 3.34746673 Simplifying a = 3.34746673Subproblem 2
a + -1.375 = -1.97246673 Simplifying a + -1.375 = -1.97246673 Reorder the terms: -1.375 + a = -1.97246673 Solving -1.375 + a = -1.97246673 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 = -1.97246673 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + a = -1.97246673 + 1.375 a = -1.97246673 + 1.375 Combine like terms: -1.97246673 + 1.375 = -0.59746673 a = -0.59746673 Simplifying a = -0.59746673Solution
The solution to the problem is based on the solutions from the subproblems. a = {3.34746673, -0.59746673}
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