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Simplifying -1a2 + -9a + 2 = 0 Reorder the terms: 2 + -9a + -1a2 = 0 Solving 2 + -9a + -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'. -2 + 9a + a2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 9a + 2 + a2 = 0 + 2 Reorder the terms: -2 + 2 + 9a + a2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 9a + a2 = 0 + 2 9a + a2 = 0 + 2 Combine like terms: 0 + 2 = 2 9a + a2 = 2 The a term is 9a. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9a + 20.25 + a2 = 2 + 20.25 Reorder the terms: 20.25 + 9a + a2 = 2 + 20.25 Combine like terms: 2 + 20.25 = 22.25 20.25 + 9a + a2 = 22.25 Factor a perfect square on the left side: (a + 4.5)(a + 4.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (a + 4.5) equal to 4.716990566 and -4.716990566.Subproblem 1
a + 4.5 = 4.716990566 Simplifying a + 4.5 = 4.716990566 Reorder the terms: 4.5 + a = 4.716990566 Solving 4.5 + a = 4.716990566 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + a = 4.716990566 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + a = 4.716990566 + -4.5 a = 4.716990566 + -4.5 Combine like terms: 4.716990566 + -4.5 = 0.216990566 a = 0.216990566 Simplifying a = 0.216990566Subproblem 2
a + 4.5 = -4.716990566 Simplifying a + 4.5 = -4.716990566 Reorder the terms: 4.5 + a = -4.716990566 Solving 4.5 + a = -4.716990566 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + a = -4.716990566 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + a = -4.716990566 + -4.5 a = -4.716990566 + -4.5 Combine like terms: -4.716990566 + -4.5 = -9.216990566 a = -9.216990566 Simplifying a = -9.216990566Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.216990566, -9.216990566}
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