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Simplifying 5 = a2 + 6a Reorder the terms: 5 = 6a + a2 Solving 5 = 6a + a2 Solving for variable 'a'. Reorder the terms: 5 + -6a + -1a2 = 6a + -6a + a2 + -1a2 Combine like terms: 6a + -6a = 0 5 + -6a + -1a2 = 0 + a2 + -1a2 5 + -6a + -1a2 = a2 + -1a2 Combine like terms: a2 + -1a2 = 0 5 + -6a + -1a2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + 6a + a2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 6a + 5 + a2 = 0 + 5 Reorder the terms: -5 + 5 + 6a + a2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 6a + a2 = 0 + 5 6a + a2 = 0 + 5 Combine like terms: 0 + 5 = 5 6a + a2 = 5 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 = 5 + 9 Reorder the terms: 9 + 6a + a2 = 5 + 9 Combine like terms: 5 + 9 = 14 9 + 6a + a2 = 14 Factor a perfect square on the left side: (a + 3)(a + 3) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (a + 3) equal to 3.741657387 and -3.741657387.Subproblem 1
a + 3 = 3.741657387 Simplifying a + 3 = 3.741657387 Reorder the terms: 3 + a = 3.741657387 Solving 3 + a = 3.741657387 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 = 3.741657387 + -3 Combine like terms: 3 + -3 = 0 0 + a = 3.741657387 + -3 a = 3.741657387 + -3 Combine like terms: 3.741657387 + -3 = 0.741657387 a = 0.741657387 Simplifying a = 0.741657387Subproblem 2
a + 3 = -3.741657387 Simplifying a + 3 = -3.741657387 Reorder the terms: 3 + a = -3.741657387 Solving 3 + a = -3.741657387 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 = -3.741657387 + -3 Combine like terms: 3 + -3 = 0 0 + a = -3.741657387 + -3 a = -3.741657387 + -3 Combine like terms: -3.741657387 + -3 = -6.741657387 a = -6.741657387 Simplifying a = -6.741657387Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.741657387, -6.741657387}
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