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Simplifying -2a2 + -46a + 252 = 0 Reorder the terms: 252 + -46a + -2a2 = 0 Solving 252 + -46a + -2a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(126 + -23a + -1a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(126 + -23a + -1a2)' equal to zero and attempt to solve: Simplifying 126 + -23a + -1a2 = 0 Solving 126 + -23a + -1a2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -126 + 23a + a2 = 0 Move the constant term to the right: Add '126' to each side of the equation. -126 + 23a + 126 + a2 = 0 + 126 Reorder the terms: -126 + 126 + 23a + a2 = 0 + 126 Combine like terms: -126 + 126 = 0 0 + 23a + a2 = 0 + 126 23a + a2 = 0 + 126 Combine like terms: 0 + 126 = 126 23a + a2 = 126 The a term is 23a. Take half its coefficient (11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. 23a + 132.25 + a2 = 126 + 132.25 Reorder the terms: 132.25 + 23a + a2 = 126 + 132.25 Combine like terms: 126 + 132.25 = 258.25 132.25 + 23a + a2 = 258.25 Factor a perfect square on the left side: (a + 11.5)(a + 11.5) = 258.25 Calculate the square root of the right side: 16.07015868 Break this problem into two subproblems by setting (a + 11.5) equal to 16.07015868 and -16.07015868.Subproblem 1
a + 11.5 = 16.07015868 Simplifying a + 11.5 = 16.07015868 Reorder the terms: 11.5 + a = 16.07015868 Solving 11.5 + a = 16.07015868 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + a = 16.07015868 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + a = 16.07015868 + -11.5 a = 16.07015868 + -11.5 Combine like terms: 16.07015868 + -11.5 = 4.57015868 a = 4.57015868 Simplifying a = 4.57015868Subproblem 2
a + 11.5 = -16.07015868 Simplifying a + 11.5 = -16.07015868 Reorder the terms: 11.5 + a = -16.07015868 Solving 11.5 + a = -16.07015868 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + a = -16.07015868 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + a = -16.07015868 + -11.5 a = -16.07015868 + -11.5 Combine like terms: -16.07015868 + -11.5 = -27.57015868 a = -27.57015868 Simplifying a = -27.57015868Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.57015868, -27.57015868}Solution
a = {4.57015868, -27.57015868}
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