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Simplifying 9a2 + a + -30 = 0 Reorder the terms: -30 + a + 9a2 = 0 Solving -30 + a + 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'. -3.333333333 + 0.1111111111a + a2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + 0.1111111111a + 3.333333333 + a2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + 0.1111111111a + a2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + 0.1111111111a + a2 = 0 + 3.333333333 0.1111111111a + a2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 0.1111111111a + a2 = 3.333333333 The a term is a. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.1111111111a + 0.25 + a2 = 3.333333333 + 0.25 Reorder the terms: 0.25 + 0.1111111111a + a2 = 3.333333333 + 0.25 Combine like terms: 3.333333333 + 0.25 = 3.583333333 0.25 + 0.1111111111a + a2 = 3.583333333 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = 3.583333333 Calculate the square root of the right side: 1.892969449 Break this problem into two subproblems by setting (a + 0.5) equal to 1.892969449 and -1.892969449.Subproblem 1
a + 0.5 = 1.892969449 Simplifying a + 0.5 = 1.892969449 Reorder the terms: 0.5 + a = 1.892969449 Solving 0.5 + a = 1.892969449 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = 1.892969449 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = 1.892969449 + -0.5 a = 1.892969449 + -0.5 Combine like terms: 1.892969449 + -0.5 = 1.392969449 a = 1.392969449 Simplifying a = 1.392969449Subproblem 2
a + 0.5 = -1.892969449 Simplifying a + 0.5 = -1.892969449 Reorder the terms: 0.5 + a = -1.892969449 Solving 0.5 + a = -1.892969449 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = -1.892969449 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = -1.892969449 + -0.5 a = -1.892969449 + -0.5 Combine like terms: -1.892969449 + -0.5 = -2.392969449 a = -2.392969449 Simplifying a = -2.392969449Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.392969449, -2.392969449}
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