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Simplifying 4a2 + -3a + -16 = 0 Reorder the terms: -16 + -3a + 4a2 = 0 Solving -16 + -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'. -4 + -0.75a + a2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -0.75a + 4 + a2 = 0 + 4 Reorder the terms: -4 + 4 + -0.75a + a2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -0.75a + a2 = 0 + 4 -0.75a + a2 = 0 + 4 Combine like terms: 0 + 4 = 4 -0.75a + a2 = 4 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 = 4 + 0.140625 Reorder the terms: 0.140625 + -0.75a + a2 = 4 + 0.140625 Combine like terms: 4 + 0.140625 = 4.140625 0.140625 + -0.75a + a2 = 4.140625 Factor a perfect square on the left side: (a + -0.375)(a + -0.375) = 4.140625 Calculate the square root of the right side: 2.034852575 Break this problem into two subproblems by setting (a + -0.375) equal to 2.034852575 and -2.034852575.Subproblem 1
a + -0.375 = 2.034852575 Simplifying a + -0.375 = 2.034852575 Reorder the terms: -0.375 + a = 2.034852575 Solving -0.375 + a = 2.034852575 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 = 2.034852575 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + a = 2.034852575 + 0.375 a = 2.034852575 + 0.375 Combine like terms: 2.034852575 + 0.375 = 2.409852575 a = 2.409852575 Simplifying a = 2.409852575Subproblem 2
a + -0.375 = -2.034852575 Simplifying a + -0.375 = -2.034852575 Reorder the terms: -0.375 + a = -2.034852575 Solving -0.375 + a = -2.034852575 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 = -2.034852575 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + a = -2.034852575 + 0.375 a = -2.034852575 + 0.375 Combine like terms: -2.034852575 + 0.375 = -1.659852575 a = -1.659852575 Simplifying a = -1.659852575Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.409852575, -1.659852575}
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