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Simplifying a2 + -18a + -48 = 0 Reorder the terms: -48 + -18a + a2 = 0 Solving -48 + -18a + 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 + -18a + 48 + a2 = 0 + 48 Reorder the terms: -48 + 48 + -18a + a2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + -18a + a2 = 0 + 48 -18a + a2 = 0 + 48 Combine like terms: 0 + 48 = 48 -18a + a2 = 48 The a term is -18a. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18a + 81 + a2 = 48 + 81 Reorder the terms: 81 + -18a + a2 = 48 + 81 Combine like terms: 48 + 81 = 129 81 + -18a + a2 = 129 Factor a perfect square on the left side: (a + -9)(a + -9) = 129 Calculate the square root of the right side: 11.357816692 Break this problem into two subproblems by setting (a + -9) equal to 11.357816692 and -11.357816692.Subproblem 1
a + -9 = 11.357816692 Simplifying a + -9 = 11.357816692 Reorder the terms: -9 + a = 11.357816692 Solving -9 + a = 11.357816692 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + a = 11.357816692 + 9 Combine like terms: -9 + 9 = 0 0 + a = 11.357816692 + 9 a = 11.357816692 + 9 Combine like terms: 11.357816692 + 9 = 20.357816692 a = 20.357816692 Simplifying a = 20.357816692Subproblem 2
a + -9 = -11.357816692 Simplifying a + -9 = -11.357816692 Reorder the terms: -9 + a = -11.357816692 Solving -9 + a = -11.357816692 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + a = -11.357816692 + 9 Combine like terms: -9 + 9 = 0 0 + a = -11.357816692 + 9 a = -11.357816692 + 9 Combine like terms: -11.357816692 + 9 = -2.357816692 a = -2.357816692 Simplifying a = -2.357816692Solution
The solution to the problem is based on the solutions from the subproblems. a = {20.357816692, -2.357816692}
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