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Simplifying 2a2 + -9a = 350 Reorder the terms: -9a + 2a2 = 350 Solving -9a + 2a2 = 350 Solving for variable 'a'. Reorder the terms: -350 + -9a + 2a2 = 350 + -350 Combine like terms: 350 + -350 = 0 -350 + -9a + 2a2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -175 + -4.5a + a2 = 0 Move the constant term to the right: Add '175' to each side of the equation. -175 + -4.5a + 175 + a2 = 0 + 175 Reorder the terms: -175 + 175 + -4.5a + a2 = 0 + 175 Combine like terms: -175 + 175 = 0 0 + -4.5a + a2 = 0 + 175 -4.5a + a2 = 0 + 175 Combine like terms: 0 + 175 = 175 -4.5a + a2 = 175 The a term is -4.5a. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5a + 5.0625 + a2 = 175 + 5.0625 Reorder the terms: 5.0625 + -4.5a + a2 = 175 + 5.0625 Combine like terms: 175 + 5.0625 = 180.0625 5.0625 + -4.5a + a2 = 180.0625 Factor a perfect square on the left side: (a + -2.25)(a + -2.25) = 180.0625 Calculate the square root of the right side: 13.4187369 Break this problem into two subproblems by setting (a + -2.25) equal to 13.4187369 and -13.4187369.Subproblem 1
a + -2.25 = 13.4187369 Simplifying a + -2.25 = 13.4187369 Reorder the terms: -2.25 + a = 13.4187369 Solving -2.25 + a = 13.4187369 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + a = 13.4187369 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + a = 13.4187369 + 2.25 a = 13.4187369 + 2.25 Combine like terms: 13.4187369 + 2.25 = 15.6687369 a = 15.6687369 Simplifying a = 15.6687369Subproblem 2
a + -2.25 = -13.4187369 Simplifying a + -2.25 = -13.4187369 Reorder the terms: -2.25 + a = -13.4187369 Solving -2.25 + a = -13.4187369 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + a = -13.4187369 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + a = -13.4187369 + 2.25 a = -13.4187369 + 2.25 Combine like terms: -13.4187369 + 2.25 = -11.1687369 a = -11.1687369 Simplifying a = -11.1687369Solution
The solution to the problem is based on the solutions from the subproblems. a = {15.6687369, -11.1687369}
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