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Simplifying -3287.3 + 523.1a + -7.5a2 = 0 Solving -3287.3 + 523.1a + -7.5a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by -7.5 the coefficient of the squared term: Divide each side by '-7.5'. 438.3066667 + -69.74666667a + a2 = 0 Move the constant term to the right: Add '-438.3066667' to each side of the equation. 438.3066667 + -69.74666667a + -438.3066667 + a2 = 0 + -438.3066667 Reorder the terms: 438.3066667 + -438.3066667 + -69.74666667a + a2 = 0 + -438.3066667 Combine like terms: 438.3066667 + -438.3066667 = 0.0000000 0.0000000 + -69.74666667a + a2 = 0 + -438.3066667 -69.74666667a + a2 = 0 + -438.3066667 Combine like terms: 0 + -438.3066667 = -438.3066667 -69.74666667a + a2 = -438.3066667 The a term is -69.74666667a. Take half its coefficient (-34.87333334). Square it (1216.149378) and add it to both sides. Add '1216.149378' to each side of the equation. -69.74666667a + 1216.149378 + a2 = -438.3066667 + 1216.149378 Reorder the terms: 1216.149378 + -69.74666667a + a2 = -438.3066667 + 1216.149378 Combine like terms: -438.3066667 + 1216.149378 = 777.8427113 1216.149378 + -69.74666667a + a2 = 777.8427113 Factor a perfect square on the left side: (a + -34.87333334)(a + -34.87333334) = 777.8427113 Calculate the square root of the right side: 27.889831683 Break this problem into two subproblems by setting (a + -34.87333334) equal to 27.889831683 and -27.889831683.Subproblem 1
a + -34.87333334 = 27.889831683 Simplifying a + -34.87333334 = 27.889831683 Reorder the terms: -34.87333334 + a = 27.889831683 Solving -34.87333334 + a = 27.889831683 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '34.87333334' to each side of the equation. -34.87333334 + 34.87333334 + a = 27.889831683 + 34.87333334 Combine like terms: -34.87333334 + 34.87333334 = 0.00000000 0.00000000 + a = 27.889831683 + 34.87333334 a = 27.889831683 + 34.87333334 Combine like terms: 27.889831683 + 34.87333334 = 62.763165023 a = 62.763165023 Simplifying a = 62.763165023Subproblem 2
a + -34.87333334 = -27.889831683 Simplifying a + -34.87333334 = -27.889831683 Reorder the terms: -34.87333334 + a = -27.889831683 Solving -34.87333334 + a = -27.889831683 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '34.87333334' to each side of the equation. -34.87333334 + 34.87333334 + a = -27.889831683 + 34.87333334 Combine like terms: -34.87333334 + 34.87333334 = 0.00000000 0.00000000 + a = -27.889831683 + 34.87333334 a = -27.889831683 + 34.87333334 Combine like terms: -27.889831683 + 34.87333334 = 6.983501657 a = 6.983501657 Simplifying a = 6.983501657Solution
The solution to the problem is based on the solutions from the subproblems. a = {62.763165023, 6.983501657}
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