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Simplifying 10 = a2 + 6a + 9 Reorder the terms: 10 = 9 + 6a + a2 Solving 10 = 9 + 6a + a2 Solving for variable 'a'. Combine like terms: 10 + -9 = 1 1 + -6a + -1a2 = 9 + 6a + a2 + -9 + -6a + -1a2 Reorder the terms: 1 + -6a + -1a2 = 9 + -9 + 6a + -6a + a2 + -1a2 Combine like terms: 9 + -9 = 0 1 + -6a + -1a2 = 0 + 6a + -6a + a2 + -1a2 1 + -6a + -1a2 = 6a + -6a + a2 + -1a2 Combine like terms: 6a + -6a = 0 1 + -6a + -1a2 = 0 + a2 + -1a2 1 + -6a + -1a2 = a2 + -1a2 Combine like terms: a2 + -1a2 = 0 1 + -6a + -1a2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1 + 6a + a2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 6a + 1 + a2 = 0 + 1 Reorder the terms: -1 + 1 + 6a + a2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 6a + a2 = 0 + 1 6a + a2 = 0 + 1 Combine like terms: 0 + 1 = 1 6a + a2 = 1 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 = 1 + 9 Reorder the terms: 9 + 6a + a2 = 1 + 9 Combine like terms: 1 + 9 = 10 9 + 6a + a2 = 10 Factor a perfect square on the left side: (a + 3)(a + 3) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (a + 3) equal to 3.16227766 and -3.16227766.Subproblem 1
a + 3 = 3.16227766 Simplifying a + 3 = 3.16227766 Reorder the terms: 3 + a = 3.16227766 Solving 3 + a = 3.16227766 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 = 3.16227766 + -3 Combine like terms: 3 + -3 = 0 0 + a = 3.16227766 + -3 a = 3.16227766 + -3 Combine like terms: 3.16227766 + -3 = 0.16227766 a = 0.16227766 Simplifying a = 0.16227766Subproblem 2
a + 3 = -3.16227766 Simplifying a + 3 = -3.16227766 Reorder the terms: 3 + a = -3.16227766 Solving 3 + a = -3.16227766 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 = -3.16227766 + -3 Combine like terms: 3 + -3 = 0 0 + a = -3.16227766 + -3 a = -3.16227766 + -3 Combine like terms: -3.16227766 + -3 = -6.16227766 a = -6.16227766 Simplifying a = -6.16227766Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.16227766, -6.16227766}
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