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Simplifying 4a2 + -3a + -3 = 0 Reorder the terms: -3 + -3a + 4a2 = 0 Solving -3 + -3a + 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'. -0.75 + -0.75a + a2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -0.75a + 0.75 + a2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -0.75a + a2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -0.75a + a2 = 0 + 0.75 -0.75a + a2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -0.75a + a2 = 0.75 The a term is -0.75a. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75a + 0.140625 + a2 = 0.75 + 0.140625 Reorder the terms: 0.140625 + -0.75a + a2 = 0.75 + 0.140625 Combine like terms: 0.75 + 0.140625 = 0.890625 0.140625 + -0.75a + a2 = 0.890625 Factor a perfect square on the left side: (a + -0.375)(a + -0.375) = 0.890625 Calculate the square root of the right side: 0.943729304 Break this problem into two subproblems by setting (a + -0.375) equal to 0.943729304 and -0.943729304.Subproblem 1
a + -0.375 = 0.943729304 Simplifying a + -0.375 = 0.943729304 Reorder the terms: -0.375 + a = 0.943729304 Solving -0.375 + a = 0.943729304 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + a = 0.943729304 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + a = 0.943729304 + 0.375 a = 0.943729304 + 0.375 Combine like terms: 0.943729304 + 0.375 = 1.318729304 a = 1.318729304 Simplifying a = 1.318729304Subproblem 2
a + -0.375 = -0.943729304 Simplifying a + -0.375 = -0.943729304 Reorder the terms: -0.375 + a = -0.943729304 Solving -0.375 + a = -0.943729304 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + a = -0.943729304 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + a = -0.943729304 + 0.375 a = -0.943729304 + 0.375 Combine like terms: -0.943729304 + 0.375 = -0.568729304 a = -0.568729304 Simplifying a = -0.568729304Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.318729304, -0.568729304}
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