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Simplifying a2 + -14a + 2 = 8 Reorder the terms: 2 + -14a + a2 = 8 Solving 2 + -14a + a2 = 8 Solving for variable 'a'. Reorder the terms: 2 + -8 + -14a + a2 = 8 + -8 Combine like terms: 2 + -8 = -6 -6 + -14a + a2 = 8 + -8 Combine like terms: 8 + -8 = 0 -6 + -14a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -14a + 6 + a2 = 0 + 6 Reorder the terms: -6 + 6 + -14a + a2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -14a + a2 = 0 + 6 -14a + a2 = 0 + 6 Combine like terms: 0 + 6 = 6 -14a + a2 = 6 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 = 6 + 49 Reorder the terms: 49 + -14a + a2 = 6 + 49 Combine like terms: 6 + 49 = 55 49 + -14a + a2 = 55 Factor a perfect square on the left side: (a + -7)(a + -7) = 55 Calculate the square root of the right side: 7.416198487 Break this problem into two subproblems by setting (a + -7) equal to 7.416198487 and -7.416198487.Subproblem 1
a + -7 = 7.416198487 Simplifying a + -7 = 7.416198487 Reorder the terms: -7 + a = 7.416198487 Solving -7 + a = 7.416198487 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 = 7.416198487 + 7 Combine like terms: -7 + 7 = 0 0 + a = 7.416198487 + 7 a = 7.416198487 + 7 Combine like terms: 7.416198487 + 7 = 14.416198487 a = 14.416198487 Simplifying a = 14.416198487Subproblem 2
a + -7 = -7.416198487 Simplifying a + -7 = -7.416198487 Reorder the terms: -7 + a = -7.416198487 Solving -7 + a = -7.416198487 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 = -7.416198487 + 7 Combine like terms: -7 + 7 = 0 0 + a = -7.416198487 + 7 a = -7.416198487 + 7 Combine like terms: -7.416198487 + 7 = -0.416198487 a = -0.416198487 Simplifying a = -0.416198487Solution
The solution to the problem is based on the solutions from the subproblems. a = {14.416198487, -0.416198487}
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