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Simplifying 9a2 + 18a + -17 = 0 Reorder the terms: -17 + 18a + 9a2 = 0 Solving -17 + 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'. -1.888888889 + 2a + a2 = 0 Move the constant term to the right: Add '1.888888889' to each side of the equation. -1.888888889 + 2a + 1.888888889 + a2 = 0 + 1.888888889 Reorder the terms: -1.888888889 + 1.888888889 + 2a + a2 = 0 + 1.888888889 Combine like terms: -1.888888889 + 1.888888889 = 0.000000000 0.000000000 + 2a + a2 = 0 + 1.888888889 2a + a2 = 0 + 1.888888889 Combine like terms: 0 + 1.888888889 = 1.888888889 2a + a2 = 1.888888889 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 = 1.888888889 + 1 Reorder the terms: 1 + 2a + a2 = 1.888888889 + 1 Combine like terms: 1.888888889 + 1 = 2.888888889 1 + 2a + a2 = 2.888888889 Factor a perfect square on the left side: (a + 1)(a + 1) = 2.888888889 Calculate the square root of the right side: 1.699673171 Break this problem into two subproblems by setting (a + 1) equal to 1.699673171 and -1.699673171.Subproblem 1
a + 1 = 1.699673171 Simplifying a + 1 = 1.699673171 Reorder the terms: 1 + a = 1.699673171 Solving 1 + a = 1.699673171 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 = 1.699673171 + -1 Combine like terms: 1 + -1 = 0 0 + a = 1.699673171 + -1 a = 1.699673171 + -1 Combine like terms: 1.699673171 + -1 = 0.699673171 a = 0.699673171 Simplifying a = 0.699673171Subproblem 2
a + 1 = -1.699673171 Simplifying a + 1 = -1.699673171 Reorder the terms: 1 + a = -1.699673171 Solving 1 + a = -1.699673171 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 = -1.699673171 + -1 Combine like terms: 1 + -1 = 0 0 + a = -1.699673171 + -1 a = -1.699673171 + -1 Combine like terms: -1.699673171 + -1 = -2.699673171 a = -2.699673171 Simplifying a = -2.699673171Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.699673171, -2.699673171}
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