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Simplifying (a + -4)(a + 10) = -17 Reorder the terms: (-4 + a)(a + 10) = -17 Reorder the terms: (-4 + a)(10 + a) = -17 Multiply (-4 + a) * (10 + a) (-4(10 + a) + a(10 + a)) = -17 ((10 * -4 + a * -4) + a(10 + a)) = -17 ((-40 + -4a) + a(10 + a)) = -17 (-40 + -4a + (10 * a + a * a)) = -17 (-40 + -4a + (10a + a2)) = -17 Combine like terms: -4a + 10a = 6a (-40 + 6a + a2) = -17 Solving -40 + 6a + a2 = -17 Solving for variable 'a'. Reorder the terms: -40 + 17 + 6a + a2 = -17 + 17 Combine like terms: -40 + 17 = -23 -23 + 6a + a2 = -17 + 17 Combine like terms: -17 + 17 = 0 -23 + 6a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + 6a + 23 + a2 = 0 + 23 Reorder the terms: -23 + 23 + 6a + a2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + 6a + a2 = 0 + 23 6a + a2 = 0 + 23 Combine like terms: 0 + 23 = 23 6a + a2 = 23 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 = 23 + 9 Reorder the terms: 9 + 6a + a2 = 23 + 9 Combine like terms: 23 + 9 = 32 9 + 6a + a2 = 32 Factor a perfect square on the left side: (a + 3)(a + 3) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (a + 3) equal to 5.656854249 and -5.656854249.Subproblem 1
a + 3 = 5.656854249 Simplifying a + 3 = 5.656854249 Reorder the terms: 3 + a = 5.656854249 Solving 3 + a = 5.656854249 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 = 5.656854249 + -3 Combine like terms: 3 + -3 = 0 0 + a = 5.656854249 + -3 a = 5.656854249 + -3 Combine like terms: 5.656854249 + -3 = 2.656854249 a = 2.656854249 Simplifying a = 2.656854249Subproblem 2
a + 3 = -5.656854249 Simplifying a + 3 = -5.656854249 Reorder the terms: 3 + a = -5.656854249 Solving 3 + a = -5.656854249 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 = -5.656854249 + -3 Combine like terms: 3 + -3 = 0 0 + a = -5.656854249 + -3 a = -5.656854249 + -3 Combine like terms: -5.656854249 + -3 = -8.656854249 a = -8.656854249 Simplifying a = -8.656854249Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.656854249, -8.656854249}
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