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Simplifying 5 + -1a + -2 + -1a2 + -5a2 + 2a = 0 Reorder the terms: 5 + -2 + -1a + 2a + -1a2 + -5a2 = 0 Combine like terms: 5 + -2 = 3 3 + -1a + 2a + -1a2 + -5a2 = 0 Combine like terms: -1a + 2a = 1a 3 + 1a + -1a2 + -5a2 = 0 Combine like terms: -1a2 + -5a2 = -6a2 3 + 1a + -6a2 = 0 Solving 3 + 1a + -6a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -0.5 + -0.1666666667a + a2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -0.1666666667a + 0.5 + a2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -0.1666666667a + a2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -0.1666666667a + a2 = 0 + 0.5 -0.1666666667a + a2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -0.1666666667a + a2 = 0.5 The a term is -0.1666666667a. Take half its coefficient (-0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. -0.1666666667a + 0.006944444447 + a2 = 0.5 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667a + a2 = 0.5 + 0.006944444447 Combine like terms: 0.5 + 0.006944444447 = 0.506944444447 0.006944444447 + -0.1666666667a + a2 = 0.506944444447 Factor a perfect square on the left side: (a + -0.08333333335)(a + -0.08333333335) = 0.506944444447 Calculate the square root of the right side: 0.712000312 Break this problem into two subproblems by setting (a + -0.08333333335) equal to 0.712000312 and -0.712000312.Subproblem 1
a + -0.08333333335 = 0.712000312 Simplifying a + -0.08333333335 = 0.712000312 Reorder the terms: -0.08333333335 + a = 0.712000312 Solving -0.08333333335 + a = 0.712000312 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + a = 0.712000312 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + a = 0.712000312 + 0.08333333335 a = 0.712000312 + 0.08333333335 Combine like terms: 0.712000312 + 0.08333333335 = 0.79533364535 a = 0.79533364535 Simplifying a = 0.79533364535Subproblem 2
a + -0.08333333335 = -0.712000312 Simplifying a + -0.08333333335 = -0.712000312 Reorder the terms: -0.08333333335 + a = -0.712000312 Solving -0.08333333335 + a = -0.712000312 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + a = -0.712000312 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + a = -0.712000312 + 0.08333333335 a = -0.712000312 + 0.08333333335 Combine like terms: -0.712000312 + 0.08333333335 = -0.62866697865 a = -0.62866697865 Simplifying a = -0.62866697865Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.79533364535, -0.62866697865}
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