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Simplifying (6a + -4a2) + (8 + 9a) = 0 Remove parenthesis around (6a + -4a2) 6a + -4a2 + (8 + 9a) = 0 Remove parenthesis around (8 + 9a) 6a + -4a2 + 8 + 9a = 0 Reorder the terms: 8 + 6a + 9a + -4a2 = 0 Combine like terms: 6a + 9a = 15a 8 + 15a + -4a2 = 0 Solving 8 + 15a + -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 + -3.75a + a2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -3.75a + 2 + a2 = 0 + 2 Reorder the terms: -2 + 2 + -3.75a + a2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3.75a + a2 = 0 + 2 -3.75a + a2 = 0 + 2 Combine like terms: 0 + 2 = 2 -3.75a + a2 = 2 The a term is -3.75a. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75a + 3.515625 + a2 = 2 + 3.515625 Reorder the terms: 3.515625 + -3.75a + a2 = 2 + 3.515625 Combine like terms: 2 + 3.515625 = 5.515625 3.515625 + -3.75a + a2 = 5.515625 Factor a perfect square on the left side: (a + -1.875)(a + -1.875) = 5.515625 Calculate the square root of the right side: 2.348536779 Break this problem into two subproblems by setting (a + -1.875) equal to 2.348536779 and -2.348536779.Subproblem 1
a + -1.875 = 2.348536779 Simplifying a + -1.875 = 2.348536779 Reorder the terms: -1.875 + a = 2.348536779 Solving -1.875 + a = 2.348536779 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + a = 2.348536779 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + a = 2.348536779 + 1.875 a = 2.348536779 + 1.875 Combine like terms: 2.348536779 + 1.875 = 4.223536779 a = 4.223536779 Simplifying a = 4.223536779Subproblem 2
a + -1.875 = -2.348536779 Simplifying a + -1.875 = -2.348536779 Reorder the terms: -1.875 + a = -2.348536779 Solving -1.875 + a = -2.348536779 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + a = -2.348536779 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + a = -2.348536779 + 1.875 a = -2.348536779 + 1.875 Combine like terms: -2.348536779 + 1.875 = -0.473536779 a = -0.473536779 Simplifying a = -0.473536779Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.223536779, -0.473536779}
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