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Simplifying a2 + 17a + -336 = 0 Reorder the terms: -336 + 17a + a2 = 0 Solving -336 + 17a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '336' to each side of the equation. -336 + 17a + 336 + a2 = 0 + 336 Reorder the terms: -336 + 336 + 17a + a2 = 0 + 336 Combine like terms: -336 + 336 = 0 0 + 17a + a2 = 0 + 336 17a + a2 = 0 + 336 Combine like terms: 0 + 336 = 336 17a + a2 = 336 The a term is 17a. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17a + 72.25 + a2 = 336 + 72.25 Reorder the terms: 72.25 + 17a + a2 = 336 + 72.25 Combine like terms: 336 + 72.25 = 408.25 72.25 + 17a + a2 = 408.25 Factor a perfect square on the left side: (a + 8.5)(a + 8.5) = 408.25 Calculate the square root of the right side: 20.205197351 Break this problem into two subproblems by setting (a + 8.5) equal to 20.205197351 and -20.205197351.Subproblem 1
a + 8.5 = 20.205197351 Simplifying a + 8.5 = 20.205197351 Reorder the terms: 8.5 + a = 20.205197351 Solving 8.5 + a = 20.205197351 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + a = 20.205197351 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + a = 20.205197351 + -8.5 a = 20.205197351 + -8.5 Combine like terms: 20.205197351 + -8.5 = 11.705197351 a = 11.705197351 Simplifying a = 11.705197351Subproblem 2
a + 8.5 = -20.205197351 Simplifying a + 8.5 = -20.205197351 Reorder the terms: 8.5 + a = -20.205197351 Solving 8.5 + a = -20.205197351 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + a = -20.205197351 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + a = -20.205197351 + -8.5 a = -20.205197351 + -8.5 Combine like terms: -20.205197351 + -8.5 = -28.705197351 a = -28.705197351 Simplifying a = -28.705197351Solution
The solution to the problem is based on the solutions from the subproblems. a = {11.705197351, -28.705197351}
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