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Simplifying a2 + -6a + -51 = 0 Reorder the terms: -51 + -6a + a2 = 0 Solving -51 + -6a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '51' to each side of the equation. -51 + -6a + 51 + a2 = 0 + 51 Reorder the terms: -51 + 51 + -6a + a2 = 0 + 51 Combine like terms: -51 + 51 = 0 0 + -6a + a2 = 0 + 51 -6a + a2 = 0 + 51 Combine like terms: 0 + 51 = 51 -6a + a2 = 51 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 = 51 + 9 Reorder the terms: 9 + -6a + a2 = 51 + 9 Combine like terms: 51 + 9 = 60 9 + -6a + a2 = 60 Factor a perfect square on the left side: (a + -3)(a + -3) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (a + -3) equal to 7.745966692 and -7.745966692.Subproblem 1
a + -3 = 7.745966692 Simplifying a + -3 = 7.745966692 Reorder the terms: -3 + a = 7.745966692 Solving -3 + a = 7.745966692 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 = 7.745966692 + 3 Combine like terms: -3 + 3 = 0 0 + a = 7.745966692 + 3 a = 7.745966692 + 3 Combine like terms: 7.745966692 + 3 = 10.745966692 a = 10.745966692 Simplifying a = 10.745966692Subproblem 2
a + -3 = -7.745966692 Simplifying a + -3 = -7.745966692 Reorder the terms: -3 + a = -7.745966692 Solving -3 + a = -7.745966692 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 = -7.745966692 + 3 Combine like terms: -3 + 3 = 0 0 + a = -7.745966692 + 3 a = -7.745966692 + 3 Combine like terms: -7.745966692 + 3 = -4.745966692 a = -4.745966692 Simplifying a = -4.745966692Solution
The solution to the problem is based on the solutions from the subproblems. a = {10.745966692, -4.745966692}
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