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Simplifying a(a + 0.954768) = 0.668338 Reorder the terms: a(0.954768 + a) = 0.668338 (0.954768 * a + a * a) = 0.668338 (0.954768a + a2) = 0.668338 Solving 0.954768a + a2 = 0.668338 Solving for variable 'a'. Reorder the terms: -0.668338 + 0.954768a + a2 = 0.668338 + -0.668338 Combine like terms: 0.668338 + -0.668338 = 0.000000 -0.668338 + 0.954768a + a2 = 0.000000 Begin completing the square. Move the constant term to the right: Add '0.668338' to each side of the equation. -0.668338 + 0.954768a + 0.668338 + a2 = 0.000000 + 0.668338 Reorder the terms: -0.668338 + 0.668338 + 0.954768a + a2 = 0.000000 + 0.668338 Combine like terms: -0.668338 + 0.668338 = 0.000000 0.000000 + 0.954768a + a2 = 0.000000 + 0.668338 0.954768a + a2 = 0.000000 + 0.668338 Combine like terms: 0.000000 + 0.668338 = 0.668338 0.954768a + a2 = 0.668338 The a term is 0.954768a. Take half its coefficient (0.477384). Square it (0.2278954835) and add it to both sides. Add '0.2278954835' to each side of the equation. 0.954768a + 0.2278954835 + a2 = 0.668338 + 0.2278954835 Reorder the terms: 0.2278954835 + 0.954768a + a2 = 0.668338 + 0.2278954835 Combine like terms: 0.668338 + 0.2278954835 = 0.8962334835 0.2278954835 + 0.954768a + a2 = 0.8962334835 Factor a perfect square on the left side: (a + 0.477384)(a + 0.477384) = 0.8962334835 Calculate the square root of the right side: 0.946696088 Break this problem into two subproblems by setting (a + 0.477384) equal to 0.946696088 and -0.946696088.Subproblem 1
a + 0.477384 = 0.946696088 Simplifying a + 0.477384 = 0.946696088 Reorder the terms: 0.477384 + a = 0.946696088 Solving 0.477384 + a = 0.946696088 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.477384' to each side of the equation. 0.477384 + -0.477384 + a = 0.946696088 + -0.477384 Combine like terms: 0.477384 + -0.477384 = 0.000000 0.000000 + a = 0.946696088 + -0.477384 a = 0.946696088 + -0.477384 Combine like terms: 0.946696088 + -0.477384 = 0.469312088 a = 0.469312088 Simplifying a = 0.469312088Subproblem 2
a + 0.477384 = -0.946696088 Simplifying a + 0.477384 = -0.946696088 Reorder the terms: 0.477384 + a = -0.946696088 Solving 0.477384 + a = -0.946696088 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.477384' to each side of the equation. 0.477384 + -0.477384 + a = -0.946696088 + -0.477384 Combine like terms: 0.477384 + -0.477384 = 0.000000 0.000000 + a = -0.946696088 + -0.477384 a = -0.946696088 + -0.477384 Combine like terms: -0.946696088 + -0.477384 = -1.424080088 a = -1.424080088 Simplifying a = -1.424080088Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.469312088, -1.424080088}
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