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Simplifying 58a2 + -9a + -30 = 0 Reorder the terms: -30 + -9a + 58a2 = 0 Solving -30 + -9a + 58a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 58 the coefficient of the squared term: Divide each side by '58'. -0.5172413793 + -0.1551724138a + a2 = 0 Move the constant term to the right: Add '0.5172413793' to each side of the equation. -0.5172413793 + -0.1551724138a + 0.5172413793 + a2 = 0 + 0.5172413793 Reorder the terms: -0.5172413793 + 0.5172413793 + -0.1551724138a + a2 = 0 + 0.5172413793 Combine like terms: -0.5172413793 + 0.5172413793 = 0.0000000000 0.0000000000 + -0.1551724138a + a2 = 0 + 0.5172413793 -0.1551724138a + a2 = 0 + 0.5172413793 Combine like terms: 0 + 0.5172413793 = 0.5172413793 -0.1551724138a + a2 = 0.5172413793 The a term is -0.1551724138a. Take half its coefficient (-0.0775862069). Square it (0.006019619501) and add it to both sides. Add '0.006019619501' to each side of the equation. -0.1551724138a + 0.006019619501 + a2 = 0.5172413793 + 0.006019619501 Reorder the terms: 0.006019619501 + -0.1551724138a + a2 = 0.5172413793 + 0.006019619501 Combine like terms: 0.5172413793 + 0.006019619501 = 0.523260998801 0.006019619501 + -0.1551724138a + a2 = 0.523260998801 Factor a perfect square on the left side: (a + -0.0775862069)(a + -0.0775862069) = 0.523260998801 Calculate the square root of the right side: 0.723367817 Break this problem into two subproblems by setting (a + -0.0775862069) equal to 0.723367817 and -0.723367817.Subproblem 1
a + -0.0775862069 = 0.723367817 Simplifying a + -0.0775862069 = 0.723367817 Reorder the terms: -0.0775862069 + a = 0.723367817 Solving -0.0775862069 + a = 0.723367817 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.0775862069' to each side of the equation. -0.0775862069 + 0.0775862069 + a = 0.723367817 + 0.0775862069 Combine like terms: -0.0775862069 + 0.0775862069 = 0.0000000000 0.0000000000 + a = 0.723367817 + 0.0775862069 a = 0.723367817 + 0.0775862069 Combine like terms: 0.723367817 + 0.0775862069 = 0.8009540239 a = 0.8009540239 Simplifying a = 0.8009540239Subproblem 2
a + -0.0775862069 = -0.723367817 Simplifying a + -0.0775862069 = -0.723367817 Reorder the terms: -0.0775862069 + a = -0.723367817 Solving -0.0775862069 + a = -0.723367817 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.0775862069' to each side of the equation. -0.0775862069 + 0.0775862069 + a = -0.723367817 + 0.0775862069 Combine like terms: -0.0775862069 + 0.0775862069 = 0.0000000000 0.0000000000 + a = -0.723367817 + 0.0775862069 a = -0.723367817 + 0.0775862069 Combine like terms: -0.723367817 + 0.0775862069 = -0.6457816101 a = -0.6457816101 Simplifying a = -0.6457816101Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.8009540239, -0.6457816101}
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