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Simplifying a2 + -3a = 37 + 3a Reorder the terms: -3a + a2 = 37 + 3a Solving -3a + a2 = 37 + 3a Solving for variable 'a'. Reorder the terms: -37 + -3a + -3a + a2 = 37 + 3a + -37 + -3a Combine like terms: -3a + -3a = -6a -37 + -6a + a2 = 37 + 3a + -37 + -3a Reorder the terms: -37 + -6a + a2 = 37 + -37 + 3a + -3a Combine like terms: 37 + -37 = 0 -37 + -6a + a2 = 0 + 3a + -3a -37 + -6a + a2 = 3a + -3a Combine like terms: 3a + -3a = 0 -37 + -6a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '37' to each side of the equation. -37 + -6a + 37 + a2 = 0 + 37 Reorder the terms: -37 + 37 + -6a + a2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + -6a + a2 = 0 + 37 -6a + a2 = 0 + 37 Combine like terms: 0 + 37 = 37 -6a + a2 = 37 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 = 37 + 9 Reorder the terms: 9 + -6a + a2 = 37 + 9 Combine like terms: 37 + 9 = 46 9 + -6a + a2 = 46 Factor a perfect square on the left side: (a + -3)(a + -3) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (a + -3) equal to 6.782329983 and -6.782329983.Subproblem 1
a + -3 = 6.782329983 Simplifying a + -3 = 6.782329983 Reorder the terms: -3 + a = 6.782329983 Solving -3 + a = 6.782329983 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 = 6.782329983 + 3 Combine like terms: -3 + 3 = 0 0 + a = 6.782329983 + 3 a = 6.782329983 + 3 Combine like terms: 6.782329983 + 3 = 9.782329983 a = 9.782329983 Simplifying a = 9.782329983Subproblem 2
a + -3 = -6.782329983 Simplifying a + -3 = -6.782329983 Reorder the terms: -3 + a = -6.782329983 Solving -3 + a = -6.782329983 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 = -6.782329983 + 3 Combine like terms: -3 + 3 = 0 0 + a = -6.782329983 + 3 a = -6.782329983 + 3 Combine like terms: -6.782329983 + 3 = -3.782329983 a = -3.782329983 Simplifying a = -3.782329983Solution
The solution to the problem is based on the solutions from the subproblems. a = {9.782329983, -3.782329983}
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