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Simplifying 9a2 + 16a + -8 = 0 Reorder the terms: -8 + 16a + 9a2 = 0 Solving -8 + 16a + 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'. -0.8888888889 + 1.777777778a + a2 = 0 Move the constant term to the right: Add '0.8888888889' to each side of the equation. -0.8888888889 + 1.777777778a + 0.8888888889 + a2 = 0 + 0.8888888889 Reorder the terms: -0.8888888889 + 0.8888888889 + 1.777777778a + a2 = 0 + 0.8888888889 Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000 0.0000000000 + 1.777777778a + a2 = 0 + 0.8888888889 1.777777778a + a2 = 0 + 0.8888888889 Combine like terms: 0 + 0.8888888889 = 0.8888888889 1.777777778a + a2 = 0.8888888889 The a term is 1.777777778a. Take half its coefficient (0.888888889). Square it (0.7901234570) and add it to both sides. Add '0.7901234570' to each side of the equation. 1.777777778a + 0.7901234570 + a2 = 0.8888888889 + 0.7901234570 Reorder the terms: 0.7901234570 + 1.777777778a + a2 = 0.8888888889 + 0.7901234570 Combine like terms: 0.8888888889 + 0.7901234570 = 1.6790123459 0.7901234570 + 1.777777778a + a2 = 1.6790123459 Factor a perfect square on the left side: (a + 0.888888889)(a + 0.888888889) = 1.6790123459 Calculate the square root of the right side: 1.295767088 Break this problem into two subproblems by setting (a + 0.888888889) equal to 1.295767088 and -1.295767088.Subproblem 1
a + 0.888888889 = 1.295767088 Simplifying a + 0.888888889 = 1.295767088 Reorder the terms: 0.888888889 + a = 1.295767088 Solving 0.888888889 + a = 1.295767088 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.888888889' to each side of the equation. 0.888888889 + -0.888888889 + a = 1.295767088 + -0.888888889 Combine like terms: 0.888888889 + -0.888888889 = 0.000000000 0.000000000 + a = 1.295767088 + -0.888888889 a = 1.295767088 + -0.888888889 Combine like terms: 1.295767088 + -0.888888889 = 0.406878199 a = 0.406878199 Simplifying a = 0.406878199Subproblem 2
a + 0.888888889 = -1.295767088 Simplifying a + 0.888888889 = -1.295767088 Reorder the terms: 0.888888889 + a = -1.295767088 Solving 0.888888889 + a = -1.295767088 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.888888889' to each side of the equation. 0.888888889 + -0.888888889 + a = -1.295767088 + -0.888888889 Combine like terms: 0.888888889 + -0.888888889 = 0.000000000 0.000000000 + a = -1.295767088 + -0.888888889 a = -1.295767088 + -0.888888889 Combine like terms: -1.295767088 + -0.888888889 = -2.184655977 a = -2.184655977 Simplifying a = -2.184655977Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.406878199, -2.184655977}
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