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Simplifying a2 + -9 = 6a Reorder the terms: -9 + a2 = 6a Solving -9 + a2 = 6a Solving for variable 'a'. Reorder the terms: -9 + -6a + a2 = 6a + -6a Combine like terms: 6a + -6a = 0 -9 + -6a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -6a + 9 + a2 = 0 + 9 Reorder the terms: -9 + 9 + -6a + a2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -6a + a2 = 0 + 9 -6a + a2 = 0 + 9 Combine like terms: 0 + 9 = 9 -6a + a2 = 9 The a term is -6a. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6a + 9 + a2 = 9 + 9 Reorder the terms: 9 + -6a + a2 = 9 + 9 Combine like terms: 9 + 9 = 18 9 + -6a + a2 = 18 Factor a perfect square on the left side: (a + -3)(a + -3) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (a + -3) equal to 4.242640687 and -4.242640687.Subproblem 1
a + -3 = 4.242640687 Simplifying a + -3 = 4.242640687 Reorder the terms: -3 + a = 4.242640687 Solving -3 + a = 4.242640687 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + a = 4.242640687 + 3 Combine like terms: -3 + 3 = 0 0 + a = 4.242640687 + 3 a = 4.242640687 + 3 Combine like terms: 4.242640687 + 3 = 7.242640687 a = 7.242640687 Simplifying a = 7.242640687Subproblem 2
a + -3 = -4.242640687 Simplifying a + -3 = -4.242640687 Reorder the terms: -3 + a = -4.242640687 Solving -3 + a = -4.242640687 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + a = -4.242640687 + 3 Combine like terms: -3 + 3 = 0 0 + a = -4.242640687 + 3 a = -4.242640687 + 3 Combine like terms: -4.242640687 + 3 = -1.242640687 a = -1.242640687 Simplifying a = -1.242640687Solution
The solution to the problem is based on the solutions from the subproblems. a = {7.242640687, -1.242640687}
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