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Simplifying -49 + 16a2 + -1a = 0 Reorder the terms: -49 + -1a + 16a2 = 0 Solving -49 + -1a + 16a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -3.0625 + -0.0625a + a2 = 0 Move the constant term to the right: Add '3.0625' to each side of the equation. -3.0625 + -0.0625a + 3.0625 + a2 = 0 + 3.0625 Reorder the terms: -3.0625 + 3.0625 + -0.0625a + a2 = 0 + 3.0625 Combine like terms: -3.0625 + 3.0625 = 0.0000 0.0000 + -0.0625a + a2 = 0 + 3.0625 -0.0625a + a2 = 0 + 3.0625 Combine like terms: 0 + 3.0625 = 3.0625 -0.0625a + a2 = 3.0625 The a term is -0.0625a. Take half its coefficient (-0.03125). Square it (0.0009765625) and add it to both sides. Add '0.0009765625' to each side of the equation. -0.0625a + 0.0009765625 + a2 = 3.0625 + 0.0009765625 Reorder the terms: 0.0009765625 + -0.0625a + a2 = 3.0625 + 0.0009765625 Combine like terms: 3.0625 + 0.0009765625 = 3.0634765625 0.0009765625 + -0.0625a + a2 = 3.0634765625 Factor a perfect square on the left side: (a + -0.03125)(a + -0.03125) = 3.0634765625 Calculate the square root of the right side: 1.750278996 Break this problem into two subproblems by setting (a + -0.03125) equal to 1.750278996 and -1.750278996.Subproblem 1
a + -0.03125 = 1.750278996 Simplifying a + -0.03125 = 1.750278996 Reorder the terms: -0.03125 + a = 1.750278996 Solving -0.03125 + a = 1.750278996 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.03125' to each side of the equation. -0.03125 + 0.03125 + a = 1.750278996 + 0.03125 Combine like terms: -0.03125 + 0.03125 = 0.00000 0.00000 + a = 1.750278996 + 0.03125 a = 1.750278996 + 0.03125 Combine like terms: 1.750278996 + 0.03125 = 1.781528996 a = 1.781528996 Simplifying a = 1.781528996Subproblem 2
a + -0.03125 = -1.750278996 Simplifying a + -0.03125 = -1.750278996 Reorder the terms: -0.03125 + a = -1.750278996 Solving -0.03125 + a = -1.750278996 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.03125' to each side of the equation. -0.03125 + 0.03125 + a = -1.750278996 + 0.03125 Combine like terms: -0.03125 + 0.03125 = 0.00000 0.00000 + a = -1.750278996 + 0.03125 a = -1.750278996 + 0.03125 Combine like terms: -1.750278996 + 0.03125 = -1.719028996 a = -1.719028996 Simplifying a = -1.719028996Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.781528996, -1.719028996}
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