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Simplifying -5312.3 + 532.1a + -7.5a2 = 0 Solving -5312.3 + 532.1a + -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 + -70.94666667a + a2 = 0 Move the constant term to the right: Add '-708.3066667' to each side of the equation. 708.3066667 + -70.94666667a + -708.3066667 + a2 = 0 + -708.3066667 Reorder the terms: 708.3066667 + -708.3066667 + -70.94666667a + a2 = 0 + -708.3066667 Combine like terms: 708.3066667 + -708.3066667 = 0.0000000 0.0000000 + -70.94666667a + a2 = 0 + -708.3066667 -70.94666667a + a2 = 0 + -708.3066667 Combine like terms: 0 + -708.3066667 = -708.3066667 -70.94666667a + a2 = -708.3066667 The a term is -70.94666667a. Take half its coefficient (-35.47333334). Square it (1258.357378) and add it to both sides. Add '1258.357378' to each side of the equation. -70.94666667a + 1258.357378 + a2 = -708.3066667 + 1258.357378 Reorder the terms: 1258.357378 + -70.94666667a + a2 = -708.3066667 + 1258.357378 Combine like terms: -708.3066667 + 1258.357378 = 550.0507113 1258.357378 + -70.94666667a + a2 = 550.0507113 Factor a perfect square on the left side: (a + -35.47333334)(a + -35.47333334) = 550.0507113 Calculate the square root of the right side: 23.453159943 Break this problem into two subproblems by setting (a + -35.47333334) equal to 23.453159943 and -23.453159943.Subproblem 1
a + -35.47333334 = 23.453159943 Simplifying a + -35.47333334 = 23.453159943 Reorder the terms: -35.47333334 + a = 23.453159943 Solving -35.47333334 + a = 23.453159943 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '35.47333334' to each side of the equation. -35.47333334 + 35.47333334 + a = 23.453159943 + 35.47333334 Combine like terms: -35.47333334 + 35.47333334 = 0.00000000 0.00000000 + a = 23.453159943 + 35.47333334 a = 23.453159943 + 35.47333334 Combine like terms: 23.453159943 + 35.47333334 = 58.926493283 a = 58.926493283 Simplifying a = 58.926493283Subproblem 2
a + -35.47333334 = -23.453159943 Simplifying a + -35.47333334 = -23.453159943 Reorder the terms: -35.47333334 + a = -23.453159943 Solving -35.47333334 + a = -23.453159943 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '35.47333334' to each side of the equation. -35.47333334 + 35.47333334 + a = -23.453159943 + 35.47333334 Combine like terms: -35.47333334 + 35.47333334 = 0.00000000 0.00000000 + a = -23.453159943 + 35.47333334 a = -23.453159943 + 35.47333334 Combine like terms: -23.453159943 + 35.47333334 = 12.020173397 a = 12.020173397 Simplifying a = 12.020173397Solution
The solution to the problem is based on the solutions from the subproblems. a = {58.926493283, 12.020173397}
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