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Simplifying 2a2 + -3a + -4 = 0 Reorder the terms: -4 + -3a + 2a2 = 0 Solving -4 + -3a + 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 + -1.5a + a2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -1.5a + 2 + a2 = 0 + 2 Reorder the terms: -2 + 2 + -1.5a + a2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1.5a + a2 = 0 + 2 -1.5a + a2 = 0 + 2 Combine like terms: 0 + 2 = 2 -1.5a + a2 = 2 The a term is -1.5a. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5a + 0.5625 + a2 = 2 + 0.5625 Reorder the terms: 0.5625 + -1.5a + a2 = 2 + 0.5625 Combine like terms: 2 + 0.5625 = 2.5625 0.5625 + -1.5a + a2 = 2.5625 Factor a perfect square on the left side: (a + -0.75)(a + -0.75) = 2.5625 Calculate the square root of the right side: 1.600781059 Break this problem into two subproblems by setting (a + -0.75) equal to 1.600781059 and -1.600781059.Subproblem 1
a + -0.75 = 1.600781059 Simplifying a + -0.75 = 1.600781059 Reorder the terms: -0.75 + a = 1.600781059 Solving -0.75 + a = 1.600781059 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + a = 1.600781059 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + a = 1.600781059 + 0.75 a = 1.600781059 + 0.75 Combine like terms: 1.600781059 + 0.75 = 2.350781059 a = 2.350781059 Simplifying a = 2.350781059Subproblem 2
a + -0.75 = -1.600781059 Simplifying a + -0.75 = -1.600781059 Reorder the terms: -0.75 + a = -1.600781059 Solving -0.75 + a = -1.600781059 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + a = -1.600781059 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + a = -1.600781059 + 0.75 a = -1.600781059 + 0.75 Combine like terms: -1.600781059 + 0.75 = -0.850781059 a = -0.850781059 Simplifying a = -0.850781059Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.350781059, -0.850781059}
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