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Simplifying a2 + -8a + -68 = 9 Reorder the terms: -68 + -8a + a2 = 9 Solving -68 + -8a + a2 = 9 Solving for variable 'a'. Reorder the terms: -68 + -9 + -8a + a2 = 9 + -9 Combine like terms: -68 + -9 = -77 -77 + -8a + a2 = 9 + -9 Combine like terms: 9 + -9 = 0 -77 + -8a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '77' to each side of the equation. -77 + -8a + 77 + a2 = 0 + 77 Reorder the terms: -77 + 77 + -8a + a2 = 0 + 77 Combine like terms: -77 + 77 = 0 0 + -8a + a2 = 0 + 77 -8a + a2 = 0 + 77 Combine like terms: 0 + 77 = 77 -8a + a2 = 77 The a term is -8a. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8a + 16 + a2 = 77 + 16 Reorder the terms: 16 + -8a + a2 = 77 + 16 Combine like terms: 77 + 16 = 93 16 + -8a + a2 = 93 Factor a perfect square on the left side: (a + -4)(a + -4) = 93 Calculate the square root of the right side: 9.643650761 Break this problem into two subproblems by setting (a + -4) equal to 9.643650761 and -9.643650761.Subproblem 1
a + -4 = 9.643650761 Simplifying a + -4 = 9.643650761 Reorder the terms: -4 + a = 9.643650761 Solving -4 + a = 9.643650761 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + a = 9.643650761 + 4 Combine like terms: -4 + 4 = 0 0 + a = 9.643650761 + 4 a = 9.643650761 + 4 Combine like terms: 9.643650761 + 4 = 13.643650761 a = 13.643650761 Simplifying a = 13.643650761Subproblem 2
a + -4 = -9.643650761 Simplifying a + -4 = -9.643650761 Reorder the terms: -4 + a = -9.643650761 Solving -4 + a = -9.643650761 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + a = -9.643650761 + 4 Combine like terms: -4 + 4 = 0 0 + a = -9.643650761 + 4 a = -9.643650761 + 4 Combine like terms: -9.643650761 + 4 = -5.643650761 a = -5.643650761 Simplifying a = -5.643650761Solution
The solution to the problem is based on the solutions from the subproblems. a = {13.643650761, -5.643650761}
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