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Simplifying a2 + -6a + 11 = 92 Reorder the terms: 11 + -6a + a2 = 92 Solving 11 + -6a + a2 = 92 Solving for variable 'a'. Reorder the terms: 11 + -92 + -6a + a2 = 92 + -92 Combine like terms: 11 + -92 = -81 -81 + -6a + a2 = 92 + -92 Combine like terms: 92 + -92 = 0 -81 + -6a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '81' to each side of the equation. -81 + -6a + 81 + a2 = 0 + 81 Reorder the terms: -81 + 81 + -6a + a2 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + -6a + a2 = 0 + 81 -6a + a2 = 0 + 81 Combine like terms: 0 + 81 = 81 -6a + a2 = 81 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 = 81 + 9 Reorder the terms: 9 + -6a + a2 = 81 + 9 Combine like terms: 81 + 9 = 90 9 + -6a + a2 = 90 Factor a perfect square on the left side: (a + -3)(a + -3) = 90 Calculate the square root of the right side: 9.486832981 Break this problem into two subproblems by setting (a + -3) equal to 9.486832981 and -9.486832981.Subproblem 1
a + -3 = 9.486832981 Simplifying a + -3 = 9.486832981 Reorder the terms: -3 + a = 9.486832981 Solving -3 + a = 9.486832981 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 = 9.486832981 + 3 Combine like terms: -3 + 3 = 0 0 + a = 9.486832981 + 3 a = 9.486832981 + 3 Combine like terms: 9.486832981 + 3 = 12.486832981 a = 12.486832981 Simplifying a = 12.486832981Subproblem 2
a + -3 = -9.486832981 Simplifying a + -3 = -9.486832981 Reorder the terms: -3 + a = -9.486832981 Solving -3 + a = -9.486832981 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 = -9.486832981 + 3 Combine like terms: -3 + 3 = 0 0 + a = -9.486832981 + 3 a = -9.486832981 + 3 Combine like terms: -9.486832981 + 3 = -6.486832981 a = -6.486832981 Simplifying a = -6.486832981Solution
The solution to the problem is based on the solutions from the subproblems. a = {12.486832981, -6.486832981}
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