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Simplifying -1a + -1a2 + -4a + 18 = 0 Reorder the terms: 18 + -1a + -4a + -1a2 = 0 Combine like terms: -1a + -4a = -5a 18 + -5a + -1a2 = 0 Solving 18 + -5a + -1a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -18 + 5a + a2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + 5a + 18 + a2 = 0 + 18 Reorder the terms: -18 + 18 + 5a + a2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 5a + a2 = 0 + 18 5a + a2 = 0 + 18 Combine like terms: 0 + 18 = 18 5a + a2 = 18 The a term is 5a. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5a + 6.25 + a2 = 18 + 6.25 Reorder the terms: 6.25 + 5a + a2 = 18 + 6.25 Combine like terms: 18 + 6.25 = 24.25 6.25 + 5a + a2 = 24.25 Factor a perfect square on the left side: (a + 2.5)(a + 2.5) = 24.25 Calculate the square root of the right side: 4.924428901 Break this problem into two subproblems by setting (a + 2.5) equal to 4.924428901 and -4.924428901.Subproblem 1
a + 2.5 = 4.924428901 Simplifying a + 2.5 = 4.924428901 Reorder the terms: 2.5 + a = 4.924428901 Solving 2.5 + a = 4.924428901 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + a = 4.924428901 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + a = 4.924428901 + -2.5 a = 4.924428901 + -2.5 Combine like terms: 4.924428901 + -2.5 = 2.424428901 a = 2.424428901 Simplifying a = 2.424428901Subproblem 2
a + 2.5 = -4.924428901 Simplifying a + 2.5 = -4.924428901 Reorder the terms: 2.5 + a = -4.924428901 Solving 2.5 + a = -4.924428901 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + a = -4.924428901 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + a = -4.924428901 + -2.5 a = -4.924428901 + -2.5 Combine like terms: -4.924428901 + -2.5 = -7.424428901 a = -7.424428901 Simplifying a = -7.424428901Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.424428901, -7.424428901}
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