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Simplifying -5312.3 + 523.1a + -7.5a2 = 0 Solving -5312.3 + 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'. 708.3066667 + -69.74666667a + a2 = 0 Move the constant term to the right: Add '-708.3066667' to each side of the equation. 708.3066667 + -69.74666667a + -708.3066667 + a2 = 0 + -708.3066667 Reorder the terms: 708.3066667 + -708.3066667 + -69.74666667a + a2 = 0 + -708.3066667 Combine like terms: 708.3066667 + -708.3066667 = 0.0000000 0.0000000 + -69.74666667a + a2 = 0 + -708.3066667 -69.74666667a + a2 = 0 + -708.3066667 Combine like terms: 0 + -708.3066667 = -708.3066667 -69.74666667a + a2 = -708.3066667 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 = -708.3066667 + 1216.149378 Reorder the terms: 1216.149378 + -69.74666667a + a2 = -708.3066667 + 1216.149378 Combine like terms: -708.3066667 + 1216.149378 = 507.8427113 1216.149378 + -69.74666667a + a2 = 507.8427113 Factor a perfect square on the left side: (a + -34.87333334)(a + -34.87333334) = 507.8427113 Calculate the square root of the right side: 22.53536579 Break this problem into two subproblems by setting (a + -34.87333334) equal to 22.53536579 and -22.53536579.Subproblem 1
a + -34.87333334 = 22.53536579 Simplifying a + -34.87333334 = 22.53536579 Reorder the terms: -34.87333334 + a = 22.53536579 Solving -34.87333334 + a = 22.53536579 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 = 22.53536579 + 34.87333334 Combine like terms: -34.87333334 + 34.87333334 = 0.00000000 0.00000000 + a = 22.53536579 + 34.87333334 a = 22.53536579 + 34.87333334 Combine like terms: 22.53536579 + 34.87333334 = 57.40869913 a = 57.40869913 Simplifying a = 57.40869913Subproblem 2
a + -34.87333334 = -22.53536579 Simplifying a + -34.87333334 = -22.53536579 Reorder the terms: -34.87333334 + a = -22.53536579 Solving -34.87333334 + a = -22.53536579 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 = -22.53536579 + 34.87333334 Combine like terms: -34.87333334 + 34.87333334 = 0.00000000 0.00000000 + a = -22.53536579 + 34.87333334 a = -22.53536579 + 34.87333334 Combine like terms: -22.53536579 + 34.87333334 = 12.33796755 a = 12.33796755 Simplifying a = 12.33796755Solution
The solution to the problem is based on the solutions from the subproblems. a = {57.40869913, 12.33796755}
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