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Simplifying a2 + -1a + -19 = 0 Reorder the terms: -19 + -1a + a2 = 0 Solving -19 + -1a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + -1a + 19 + a2 = 0 + 19 Reorder the terms: -19 + 19 + -1a + a2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -1a + a2 = 0 + 19 -1a + a2 = 0 + 19 Combine like terms: 0 + 19 = 19 -1a + a2 = 19 The a term is -1a. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1a + 0.25 + a2 = 19 + 0.25 Reorder the terms: 0.25 + -1a + a2 = 19 + 0.25 Combine like terms: 19 + 0.25 = 19.25 0.25 + -1a + a2 = 19.25 Factor a perfect square on the left side: (a + -0.5)(a + -0.5) = 19.25 Calculate the square root of the right side: 4.387482194 Break this problem into two subproblems by setting (a + -0.5) equal to 4.387482194 and -4.387482194.Subproblem 1
a + -0.5 = 4.387482194 Simplifying a + -0.5 = 4.387482194 Reorder the terms: -0.5 + a = 4.387482194 Solving -0.5 + a = 4.387482194 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + a = 4.387482194 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + a = 4.387482194 + 0.5 a = 4.387482194 + 0.5 Combine like terms: 4.387482194 + 0.5 = 4.887482194 a = 4.887482194 Simplifying a = 4.887482194Subproblem 2
a + -0.5 = -4.387482194 Simplifying a + -0.5 = -4.387482194 Reorder the terms: -0.5 + a = -4.387482194 Solving -0.5 + a = -4.387482194 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + a = -4.387482194 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + a = -4.387482194 + 0.5 a = -4.387482194 + 0.5 Combine like terms: -4.387482194 + 0.5 = -3.887482194 a = -3.887482194 Simplifying a = -3.887482194Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.887482194, -3.887482194}
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