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Simplifying 5a2 + -18a + 1 = 0 Reorder the terms: 1 + -18a + 5a2 = 0 Solving 1 + -18a + 5a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2 + -3.6a + a2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + -3.6a + -0.2 + a2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + -3.6a + a2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + -3.6a + a2 = 0 + -0.2 -3.6a + a2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 -3.6a + a2 = -0.2 The a term is -3.6a. Take half its coefficient (-1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. -3.6a + 3.24 + a2 = -0.2 + 3.24 Reorder the terms: 3.24 + -3.6a + a2 = -0.2 + 3.24 Combine like terms: -0.2 + 3.24 = 3.04 3.24 + -3.6a + a2 = 3.04 Factor a perfect square on the left side: (a + -1.8)(a + -1.8) = 3.04 Calculate the square root of the right side: 1.743559577 Break this problem into two subproblems by setting (a + -1.8) equal to 1.743559577 and -1.743559577.Subproblem 1
a + -1.8 = 1.743559577 Simplifying a + -1.8 = 1.743559577 Reorder the terms: -1.8 + a = 1.743559577 Solving -1.8 + a = 1.743559577 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + a = 1.743559577 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + a = 1.743559577 + 1.8 a = 1.743559577 + 1.8 Combine like terms: 1.743559577 + 1.8 = 3.543559577 a = 3.543559577 Simplifying a = 3.543559577Subproblem 2
a + -1.8 = -1.743559577 Simplifying a + -1.8 = -1.743559577 Reorder the terms: -1.8 + a = -1.743559577 Solving -1.8 + a = -1.743559577 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + a = -1.743559577 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + a = -1.743559577 + 1.8 a = -1.743559577 + 1.8 Combine like terms: -1.743559577 + 1.8 = 0.056440423 a = 0.056440423 Simplifying a = 0.056440423Solution
The solution to the problem is based on the solutions from the subproblems. a = {3.543559577, 0.056440423}
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