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Simplifying 9a2 + 18a + 4 = 0 Reorder the terms: 4 + 18a + 9a2 = 0 Solving 4 + 18a + 9a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.4444444444 + 2a + a2 = 0 Move the constant term to the right: Add '-0.4444444444' to each side of the equation. 0.4444444444 + 2a + -0.4444444444 + a2 = 0 + -0.4444444444 Reorder the terms: 0.4444444444 + -0.4444444444 + 2a + a2 = 0 + -0.4444444444 Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000 0.0000000000 + 2a + a2 = 0 + -0.4444444444 2a + a2 = 0 + -0.4444444444 Combine like terms: 0 + -0.4444444444 = -0.4444444444 2a + a2 = -0.4444444444 The a term is 2a. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2a + 1 + a2 = -0.4444444444 + 1 Reorder the terms: 1 + 2a + a2 = -0.4444444444 + 1 Combine like terms: -0.4444444444 + 1 = 0.5555555556 1 + 2a + a2 = 0.5555555556 Factor a perfect square on the left side: (a + 1)(a + 1) = 0.5555555556 Calculate the square root of the right side: 0.745355993 Break this problem into two subproblems by setting (a + 1) equal to 0.745355993 and -0.745355993.Subproblem 1
a + 1 = 0.745355993 Simplifying a + 1 = 0.745355993 Reorder the terms: 1 + a = 0.745355993 Solving 1 + a = 0.745355993 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = 0.745355993 + -1 Combine like terms: 1 + -1 = 0 0 + a = 0.745355993 + -1 a = 0.745355993 + -1 Combine like terms: 0.745355993 + -1 = -0.254644007 a = -0.254644007 Simplifying a = -0.254644007Subproblem 2
a + 1 = -0.745355993 Simplifying a + 1 = -0.745355993 Reorder the terms: 1 + a = -0.745355993 Solving 1 + a = -0.745355993 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = -0.745355993 + -1 Combine like terms: 1 + -1 = 0 0 + a = -0.745355993 + -1 a = -0.745355993 + -1 Combine like terms: -0.745355993 + -1 = -1.745355993 a = -1.745355993 Simplifying a = -1.745355993Solution
The solution to the problem is based on the solutions from the subproblems. a = {-0.254644007, -1.745355993}
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