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Simplifying a2 + 4a + 4 = 45 Reorder the terms: 4 + 4a + a2 = 45 Solving 4 + 4a + a2 = 45 Solving for variable 'a'. Reorder the terms: 4 + -45 + 4a + a2 = 45 + -45 Combine like terms: 4 + -45 = -41 -41 + 4a + a2 = 45 + -45 Combine like terms: 45 + -45 = 0 -41 + 4a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + 4a + 41 + a2 = 0 + 41 Reorder the terms: -41 + 41 + 4a + a2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + 4a + a2 = 0 + 41 4a + a2 = 0 + 41 Combine like terms: 0 + 41 = 41 4a + a2 = 41 The a term is 4a. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4a + 4 + a2 = 41 + 4 Reorder the terms: 4 + 4a + a2 = 41 + 4 Combine like terms: 41 + 4 = 45 4 + 4a + a2 = 45 Factor a perfect square on the left side: (a + 2)(a + 2) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (a + 2) equal to 6.708203933 and -6.708203933.Subproblem 1
a + 2 = 6.708203933 Simplifying a + 2 = 6.708203933 Reorder the terms: 2 + a = 6.708203933 Solving 2 + a = 6.708203933 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + a = 6.708203933 + -2 Combine like terms: 2 + -2 = 0 0 + a = 6.708203933 + -2 a = 6.708203933 + -2 Combine like terms: 6.708203933 + -2 = 4.708203933 a = 4.708203933 Simplifying a = 4.708203933Subproblem 2
a + 2 = -6.708203933 Simplifying a + 2 = -6.708203933 Reorder the terms: 2 + a = -6.708203933 Solving 2 + a = -6.708203933 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + a = -6.708203933 + -2 Combine like terms: 2 + -2 = 0 0 + a = -6.708203933 + -2 a = -6.708203933 + -2 Combine like terms: -6.708203933 + -2 = -8.708203933 a = -8.708203933 Simplifying a = -8.708203933Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.708203933, -8.708203933}
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