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Simplifying a2 + -0.05a + 0.00006 = 0 Reorder the terms: 0.00006 + -0.05a + a2 = 0 Solving 0.00006 + -0.05a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-0.00006' to each side of the equation. 0.00006 + -0.05a + -0.00006 + a2 = 0 + -0.00006 Reorder the terms: 0.00006 + -0.00006 + -0.05a + a2 = 0 + -0.00006 Combine like terms: 0.00006 + -0.00006 = 0.00000 0.00000 + -0.05a + a2 = 0 + -0.00006 -0.05a + a2 = 0 + -0.00006 Combine like terms: 0 + -0.00006 = -0.00006 -0.05a + a2 = -0.00006 The a term is -0.05a. Take half its coefficient (-0.025). Square it (0.000625) and add it to both sides. Add '0.000625' to each side of the equation. -0.05a + 0.000625 + a2 = -0.00006 + 0.000625 Reorder the terms: 0.000625 + -0.05a + a2 = -0.00006 + 0.000625 Combine like terms: -0.00006 + 0.000625 = 0.000565 0.000625 + -0.05a + a2 = 0.000565 Factor a perfect square on the left side: (a + -0.025)(a + -0.025) = 0.000565 Calculate the square root of the right side: 0.023769729 Break this problem into two subproblems by setting (a + -0.025) equal to 0.023769729 and -0.023769729.Subproblem 1
a + -0.025 = 0.023769729 Simplifying a + -0.025 = 0.023769729 Reorder the terms: -0.025 + a = 0.023769729 Solving -0.025 + a = 0.023769729 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.025' to each side of the equation. -0.025 + 0.025 + a = 0.023769729 + 0.025 Combine like terms: -0.025 + 0.025 = 0.000 0.000 + a = 0.023769729 + 0.025 a = 0.023769729 + 0.025 Combine like terms: 0.023769729 + 0.025 = 0.048769729 a = 0.048769729 Simplifying a = 0.048769729Subproblem 2
a + -0.025 = -0.023769729 Simplifying a + -0.025 = -0.023769729 Reorder the terms: -0.025 + a = -0.023769729 Solving -0.025 + a = -0.023769729 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.025' to each side of the equation. -0.025 + 0.025 + a = -0.023769729 + 0.025 Combine like terms: -0.025 + 0.025 = 0.000 0.000 + a = -0.023769729 + 0.025 a = -0.023769729 + 0.025 Combine like terms: -0.023769729 + 0.025 = 0.001230271 a = 0.001230271 Simplifying a = 0.001230271Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.048769729, 0.001230271}
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