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Simplifying a2 + -3a + -48 = 0 Reorder the terms: -48 + -3a + a2 = 0 Solving -48 + -3a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + -3a + 48 + a2 = 0 + 48 Reorder the terms: -48 + 48 + -3a + a2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + -3a + a2 = 0 + 48 -3a + a2 = 0 + 48 Combine like terms: 0 + 48 = 48 -3a + a2 = 48 The a term is -3a. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3a + 2.25 + a2 = 48 + 2.25 Reorder the terms: 2.25 + -3a + a2 = 48 + 2.25 Combine like terms: 48 + 2.25 = 50.25 2.25 + -3a + a2 = 50.25 Factor a perfect square on the left side: (a + -1.5)(a + -1.5) = 50.25 Calculate the square root of the right side: 7.088723439 Break this problem into two subproblems by setting (a + -1.5) equal to 7.088723439 and -7.088723439.Subproblem 1
a + -1.5 = 7.088723439 Simplifying a + -1.5 = 7.088723439 Reorder the terms: -1.5 + a = 7.088723439 Solving -1.5 + a = 7.088723439 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + a = 7.088723439 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + a = 7.088723439 + 1.5 a = 7.088723439 + 1.5 Combine like terms: 7.088723439 + 1.5 = 8.588723439 a = 8.588723439 Simplifying a = 8.588723439Subproblem 2
a + -1.5 = -7.088723439 Simplifying a + -1.5 = -7.088723439 Reorder the terms: -1.5 + a = -7.088723439 Solving -1.5 + a = -7.088723439 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + a = -7.088723439 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + a = -7.088723439 + 1.5 a = -7.088723439 + 1.5 Combine like terms: -7.088723439 + 1.5 = -5.588723439 a = -5.588723439 Simplifying a = -5.588723439Solution
The solution to the problem is based on the solutions from the subproblems. a = {8.588723439, -5.588723439}
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