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Simplifying 2a2 + -5a + -4 = 0 Reorder the terms: -4 + -5a + 2a2 = 0 Solving -4 + -5a + 2a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2 + -2.5a + a2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -2.5a + 2 + a2 = 0 + 2 Reorder the terms: -2 + 2 + -2.5a + a2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -2.5a + a2 = 0 + 2 -2.5a + a2 = 0 + 2 Combine like terms: 0 + 2 = 2 -2.5a + a2 = 2 The a term is -2.5a. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5a + 1.5625 + a2 = 2 + 1.5625 Reorder the terms: 1.5625 + -2.5a + a2 = 2 + 1.5625 Combine like terms: 2 + 1.5625 = 3.5625 1.5625 + -2.5a + a2 = 3.5625 Factor a perfect square on the left side: (a + -1.25)(a + -1.25) = 3.5625 Calculate the square root of the right side: 1.887458609 Break this problem into two subproblems by setting (a + -1.25) equal to 1.887458609 and -1.887458609.Subproblem 1
a + -1.25 = 1.887458609 Simplifying a + -1.25 = 1.887458609 Reorder the terms: -1.25 + a = 1.887458609 Solving -1.25 + a = 1.887458609 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + a = 1.887458609 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + a = 1.887458609 + 1.25 a = 1.887458609 + 1.25 Combine like terms: 1.887458609 + 1.25 = 3.137458609 a = 3.137458609 Simplifying a = 3.137458609Subproblem 2
a + -1.25 = -1.887458609 Simplifying a + -1.25 = -1.887458609 Reorder the terms: -1.25 + a = -1.887458609 Solving -1.25 + a = -1.887458609 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + a = -1.887458609 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + a = -1.887458609 + 1.25 a = -1.887458609 + 1.25 Combine like terms: -1.887458609 + 1.25 = -0.637458609 a = -0.637458609 Simplifying a = -0.637458609Solution
The solution to the problem is based on the solutions from the subproblems. a = {3.137458609, -0.637458609}
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