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Simplifying a2 + -14a + 49 = 3 Reorder the terms: 49 + -14a + a2 = 3 Solving 49 + -14a + a2 = 3 Solving for variable 'a'. Reorder the terms: 49 + -3 + -14a + a2 = 3 + -3 Combine like terms: 49 + -3 = 46 46 + -14a + a2 = 3 + -3 Combine like terms: 3 + -3 = 0 46 + -14a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-46' to each side of the equation. 46 + -14a + -46 + a2 = 0 + -46 Reorder the terms: 46 + -46 + -14a + a2 = 0 + -46 Combine like terms: 46 + -46 = 0 0 + -14a + a2 = 0 + -46 -14a + a2 = 0 + -46 Combine like terms: 0 + -46 = -46 -14a + a2 = -46 The a term is -14a. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14a + 49 + a2 = -46 + 49 Reorder the terms: 49 + -14a + a2 = -46 + 49 Combine like terms: -46 + 49 = 3 49 + -14a + a2 = 3 Factor a perfect square on the left side: (a + -7)(a + -7) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (a + -7) equal to 1.732050808 and -1.732050808.Subproblem 1
a + -7 = 1.732050808 Simplifying a + -7 = 1.732050808 Reorder the terms: -7 + a = 1.732050808 Solving -7 + a = 1.732050808 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + a = 1.732050808 + 7 Combine like terms: -7 + 7 = 0 0 + a = 1.732050808 + 7 a = 1.732050808 + 7 Combine like terms: 1.732050808 + 7 = 8.732050808 a = 8.732050808 Simplifying a = 8.732050808Subproblem 2
a + -7 = -1.732050808 Simplifying a + -7 = -1.732050808 Reorder the terms: -7 + a = -1.732050808 Solving -7 + a = -1.732050808 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + a = -1.732050808 + 7 Combine like terms: -7 + 7 = 0 0 + a = -1.732050808 + 7 a = -1.732050808 + 7 Combine like terms: -1.732050808 + 7 = 5.267949192 a = 5.267949192 Simplifying a = 5.267949192Solution
The solution to the problem is based on the solutions from the subproblems. a = {8.732050808, 5.267949192}
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