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Simplifying 4a2 + -20a + 17 = 0 Reorder the terms: 17 + -20a + 4a2 = 0 Solving 17 + -20a + 4a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 4.25 + -5a + a2 = 0 Move the constant term to the right: Add '-4.25' to each side of the equation. 4.25 + -5a + -4.25 + a2 = 0 + -4.25 Reorder the terms: 4.25 + -4.25 + -5a + a2 = 0 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + -5a + a2 = 0 + -4.25 -5a + a2 = 0 + -4.25 Combine like terms: 0 + -4.25 = -4.25 -5a + a2 = -4.25 The a term is -5a. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5a + 6.25 + a2 = -4.25 + 6.25 Reorder the terms: 6.25 + -5a + a2 = -4.25 + 6.25 Combine like terms: -4.25 + 6.25 = 2 6.25 + -5a + a2 = 2 Factor a perfect square on the left side: (a + -2.5)(a + -2.5) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (a + -2.5) equal to 1.414213562 and -1.414213562.Subproblem 1
a + -2.5 = 1.414213562 Simplifying a + -2.5 = 1.414213562 Reorder the terms: -2.5 + a = 1.414213562 Solving -2.5 + a = 1.414213562 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + a = 1.414213562 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + a = 1.414213562 + 2.5 a = 1.414213562 + 2.5 Combine like terms: 1.414213562 + 2.5 = 3.914213562 a = 3.914213562 Simplifying a = 3.914213562Subproblem 2
a + -2.5 = -1.414213562 Simplifying a + -2.5 = -1.414213562 Reorder the terms: -2.5 + a = -1.414213562 Solving -2.5 + a = -1.414213562 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + a = -1.414213562 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + a = -1.414213562 + 2.5 a = -1.414213562 + 2.5 Combine like terms: -1.414213562 + 2.5 = 1.085786438 a = 1.085786438 Simplifying a = 1.085786438Solution
The solution to the problem is based on the solutions from the subproblems. a = {3.914213562, 1.085786438}
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