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Simplifying 2a2 + -18a + 9 = 0 Reorder the terms: 9 + -18a + 2a2 = 0 Solving 9 + -18a + 2a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4.5 + -9a + a2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + -9a + -4.5 + a2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + -9a + a2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + -9a + a2 = 0 + -4.5 -9a + a2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 -9a + a2 = -4.5 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 = -4.5 + 20.25 Reorder the terms: 20.25 + -9a + a2 = -4.5 + 20.25 Combine like terms: -4.5 + 20.25 = 15.75 20.25 + -9a + a2 = 15.75 Factor a perfect square on the left side: (a + -4.5)(a + -4.5) = 15.75 Calculate the square root of the right side: 3.968626967 Break this problem into two subproblems by setting (a + -4.5) equal to 3.968626967 and -3.968626967.Subproblem 1
a + -4.5 = 3.968626967 Simplifying a + -4.5 = 3.968626967 Reorder the terms: -4.5 + a = 3.968626967 Solving -4.5 + a = 3.968626967 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 = 3.968626967 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + a = 3.968626967 + 4.5 a = 3.968626967 + 4.5 Combine like terms: 3.968626967 + 4.5 = 8.468626967 a = 8.468626967 Simplifying a = 8.468626967Subproblem 2
a + -4.5 = -3.968626967 Simplifying a + -4.5 = -3.968626967 Reorder the terms: -4.5 + a = -3.968626967 Solving -4.5 + a = -3.968626967 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 = -3.968626967 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + a = -3.968626967 + 4.5 a = -3.968626967 + 4.5 Combine like terms: -3.968626967 + 4.5 = 0.531373033 a = 0.531373033 Simplifying a = 0.531373033Solution
The solution to the problem is based on the solutions from the subproblems. a = {8.468626967, 0.531373033}
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