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Simplifying -89905.98a2 + 3239.7a + -2.25 = 0 Reorder the terms: -2.25 + 3239.7a + -89905.98a2 = 0 Solving -2.25 + 3239.7a + -89905.98a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by -89905.98 the coefficient of the squared term: Divide each side by '-89905.98'. 0.00002502614398 + -0.03603431051a + a2 = 0 Move the constant term to the right: Add '-0.00002502614398' to each side of the equation. 0.00002502614398 + -0.03603431051a + -0.00002502614398 + a2 = 0 + -0.00002502614398 Reorder the terms: 0.00002502614398 + -0.00002502614398 + -0.03603431051a + a2 = 0 + -0.00002502614398 Combine like terms: 0.00002502614398 + -0.00002502614398 = 0.00000000000000 0.00000000000000 + -0.03603431051a + a2 = 0 + -0.00002502614398 -0.03603431051a + a2 = 0 + -0.00002502614398 Combine like terms: 0 + -0.00002502614398 = -0.00002502614398 -0.03603431051a + a2 = -0.00002502614398 The a term is -0.03603431051a. Take half its coefficient (-0.01801715526). Square it (0.0003246178837) and add it to both sides. Add '0.0003246178837' to each side of the equation. -0.03603431051a + 0.0003246178837 + a2 = -0.00002502614398 + 0.0003246178837 Reorder the terms: 0.0003246178837 + -0.03603431051a + a2 = -0.00002502614398 + 0.0003246178837 Combine like terms: -0.00002502614398 + 0.0003246178837 = 0.00029959173972 0.0003246178837 + -0.03603431051a + a2 = 0.00029959173972 Factor a perfect square on the left side: (a + -0.01801715526)(a + -0.01801715526) = 0.00029959173972 Calculate the square root of the right side: 0.017308719 Break this problem into two subproblems by setting (a + -0.01801715526) equal to 0.017308719 and -0.017308719.Subproblem 1
a + -0.01801715526 = 0.017308719 Simplifying a + -0.01801715526 = 0.017308719 Reorder the terms: -0.01801715526 + a = 0.017308719 Solving -0.01801715526 + a = 0.017308719 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.01801715526' to each side of the equation. -0.01801715526 + 0.01801715526 + a = 0.017308719 + 0.01801715526 Combine like terms: -0.01801715526 + 0.01801715526 = 0.00000000000 0.00000000000 + a = 0.017308719 + 0.01801715526 a = 0.017308719 + 0.01801715526 Combine like terms: 0.017308719 + 0.01801715526 = 0.03532587426 a = 0.03532587426 Simplifying a = 0.03532587426Subproblem 2
a + -0.01801715526 = -0.017308719 Simplifying a + -0.01801715526 = -0.017308719 Reorder the terms: -0.01801715526 + a = -0.017308719 Solving -0.01801715526 + a = -0.017308719 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.01801715526' to each side of the equation. -0.01801715526 + 0.01801715526 + a = -0.017308719 + 0.01801715526 Combine like terms: -0.01801715526 + 0.01801715526 = 0.00000000000 0.00000000000 + a = -0.017308719 + 0.01801715526 a = -0.017308719 + 0.01801715526 Combine like terms: -0.017308719 + 0.01801715526 = 0.00070843626 a = 0.00070843626 Simplifying a = 0.00070843626Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.03532587426, 0.00070843626}
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