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Simplifying 36 = a2 + -6a Reorder the terms: 36 = -6a + a2 Solving 36 = -6a + a2 Solving for variable 'a'. Reorder the terms: 36 + 6a + -1a2 = -6a + 6a + a2 + -1a2 Combine like terms: -6a + 6a = 0 36 + 6a + -1a2 = 0 + a2 + -1a2 36 + 6a + -1a2 = a2 + -1a2 Combine like terms: a2 + -1a2 = 0 36 + 6a + -1a2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -36 + -6a + a2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + -6a + 36 + a2 = 0 + 36 Reorder the terms: -36 + 36 + -6a + a2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -6a + a2 = 0 + 36 -6a + a2 = 0 + 36 Combine like terms: 0 + 36 = 36 -6a + a2 = 36 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 = 36 + 9 Reorder the terms: 9 + -6a + a2 = 36 + 9 Combine like terms: 36 + 9 = 45 9 + -6a + a2 = 45 Factor a perfect square on the left side: (a + -3)(a + -3) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (a + -3) equal to 6.708203933 and -6.708203933.Subproblem 1
a + -3 = 6.708203933 Simplifying a + -3 = 6.708203933 Reorder the terms: -3 + a = 6.708203933 Solving -3 + a = 6.708203933 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 = 6.708203933 + 3 Combine like terms: -3 + 3 = 0 0 + a = 6.708203933 + 3 a = 6.708203933 + 3 Combine like terms: 6.708203933 + 3 = 9.708203933 a = 9.708203933 Simplifying a = 9.708203933Subproblem 2
a + -3 = -6.708203933 Simplifying a + -3 = -6.708203933 Reorder the terms: -3 + a = -6.708203933 Solving -3 + a = -6.708203933 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 = -6.708203933 + 3 Combine like terms: -3 + 3 = 0 0 + a = -6.708203933 + 3 a = -6.708203933 + 3 Combine like terms: -6.708203933 + 3 = -3.708203933 a = -3.708203933 Simplifying a = -3.708203933Solution
The solution to the problem is based on the solutions from the subproblems. a = {9.708203933, -3.708203933}
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