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Simplifying a2 + 40a + 22 = 0 Reorder the terms: 22 + 40a + a2 = 0 Solving 22 + 40a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-22' to each side of the equation. 22 + 40a + -22 + a2 = 0 + -22 Reorder the terms: 22 + -22 + 40a + a2 = 0 + -22 Combine like terms: 22 + -22 = 0 0 + 40a + a2 = 0 + -22 40a + a2 = 0 + -22 Combine like terms: 0 + -22 = -22 40a + a2 = -22 The a term is 40a. Take half its coefficient (20). Square it (400) and add it to both sides. Add '400' to each side of the equation. 40a + 400 + a2 = -22 + 400 Reorder the terms: 400 + 40a + a2 = -22 + 400 Combine like terms: -22 + 400 = 378 400 + 40a + a2 = 378 Factor a perfect square on the left side: (a + 20)(a + 20) = 378 Calculate the square root of the right side: 19.442222095 Break this problem into two subproblems by setting (a + 20) equal to 19.442222095 and -19.442222095.Subproblem 1
a + 20 = 19.442222095 Simplifying a + 20 = 19.442222095 Reorder the terms: 20 + a = 19.442222095 Solving 20 + a = 19.442222095 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + a = 19.442222095 + -20 Combine like terms: 20 + -20 = 0 0 + a = 19.442222095 + -20 a = 19.442222095 + -20 Combine like terms: 19.442222095 + -20 = -0.557777905 a = -0.557777905 Simplifying a = -0.557777905Subproblem 2
a + 20 = -19.442222095 Simplifying a + 20 = -19.442222095 Reorder the terms: 20 + a = -19.442222095 Solving 20 + a = -19.442222095 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + a = -19.442222095 + -20 Combine like terms: 20 + -20 = 0 0 + a = -19.442222095 + -20 a = -19.442222095 + -20 Combine like terms: -19.442222095 + -20 = -39.442222095 a = -39.442222095 Simplifying a = -39.442222095Solution
The solution to the problem is based on the solutions from the subproblems. a = {-0.557777905, -39.442222095}
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