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Simplifying a2 + -6a + 1 = 0 Reorder the terms: 1 + -6a + a2 = 0 Solving 1 + -6a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -6a + -1 + a2 = 0 + -1 Reorder the terms: 1 + -1 + -6a + a2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -6a + a2 = 0 + -1 -6a + a2 = 0 + -1 Combine like terms: 0 + -1 = -1 -6a + a2 = -1 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 = -1 + 9 Reorder the terms: 9 + -6a + a2 = -1 + 9 Combine like terms: -1 + 9 = 8 9 + -6a + a2 = 8 Factor a perfect square on the left side: (a + -3)(a + -3) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (a + -3) equal to 2.828427125 and -2.828427125.Subproblem 1
a + -3 = 2.828427125 Simplifying a + -3 = 2.828427125 Reorder the terms: -3 + a = 2.828427125 Solving -3 + a = 2.828427125 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 = 2.828427125 + 3 Combine like terms: -3 + 3 = 0 0 + a = 2.828427125 + 3 a = 2.828427125 + 3 Combine like terms: 2.828427125 + 3 = 5.828427125 a = 5.828427125 Simplifying a = 5.828427125Subproblem 2
a + -3 = -2.828427125 Simplifying a + -3 = -2.828427125 Reorder the terms: -3 + a = -2.828427125 Solving -3 + a = -2.828427125 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 = -2.828427125 + 3 Combine like terms: -3 + 3 = 0 0 + a = -2.828427125 + 3 a = -2.828427125 + 3 Combine like terms: -2.828427125 + 3 = 0.171572875 a = 0.171572875 Simplifying a = 0.171572875Solution
The solution to the problem is based on the solutions from the subproblems. a = {5.828427125, 0.171572875}
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