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Simplifying (a + -10)(a + -14) = 16 Reorder the terms: (-10 + a)(a + -14) = 16 Reorder the terms: (-10 + a)(-14 + a) = 16 Multiply (-10 + a) * (-14 + a) (-10(-14 + a) + a(-14 + a)) = 16 ((-14 * -10 + a * -10) + a(-14 + a)) = 16 ((140 + -10a) + a(-14 + a)) = 16 (140 + -10a + (-14 * a + a * a)) = 16 (140 + -10a + (-14a + a2)) = 16 Combine like terms: -10a + -14a = -24a (140 + -24a + a2) = 16 Solving 140 + -24a + a2 = 16 Solving for variable 'a'. Reorder the terms: 140 + -16 + -24a + a2 = 16 + -16 Combine like terms: 140 + -16 = 124 124 + -24a + a2 = 16 + -16 Combine like terms: 16 + -16 = 0 124 + -24a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-124' to each side of the equation. 124 + -24a + -124 + a2 = 0 + -124 Reorder the terms: 124 + -124 + -24a + a2 = 0 + -124 Combine like terms: 124 + -124 = 0 0 + -24a + a2 = 0 + -124 -24a + a2 = 0 + -124 Combine like terms: 0 + -124 = -124 -24a + a2 = -124 The a term is -24a. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24a + 144 + a2 = -124 + 144 Reorder the terms: 144 + -24a + a2 = -124 + 144 Combine like terms: -124 + 144 = 20 144 + -24a + a2 = 20 Factor a perfect square on the left side: (a + -12)(a + -12) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (a + -12) equal to 4.472135955 and -4.472135955.Subproblem 1
a + -12 = 4.472135955 Simplifying a + -12 = 4.472135955 Reorder the terms: -12 + a = 4.472135955 Solving -12 + a = 4.472135955 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + a = 4.472135955 + 12 Combine like terms: -12 + 12 = 0 0 + a = 4.472135955 + 12 a = 4.472135955 + 12 Combine like terms: 4.472135955 + 12 = 16.472135955 a = 16.472135955 Simplifying a = 16.472135955Subproblem 2
a + -12 = -4.472135955 Simplifying a + -12 = -4.472135955 Reorder the terms: -12 + a = -4.472135955 Solving -12 + a = -4.472135955 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + a = -4.472135955 + 12 Combine like terms: -12 + 12 = 0 0 + a = -4.472135955 + 12 a = -4.472135955 + 12 Combine like terms: -4.472135955 + 12 = 7.527864045 a = 7.527864045 Simplifying a = 7.527864045Solution
The solution to the problem is based on the solutions from the subproblems. a = {16.472135955, 7.527864045}
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