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Simplifying 4a2 + 8a + -98 = 0 Reorder the terms: -98 + 8a + 4a2 = 0 Solving -98 + 8a + 4a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(-49 + 4a + 2a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-49 + 4a + 2a2)' equal to zero and attempt to solve: Simplifying -49 + 4a + 2a2 = 0 Solving -49 + 4a + 2a2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -24.5 + 2a + a2 = 0 Move the constant term to the right: Add '24.5' to each side of the equation. -24.5 + 2a + 24.5 + a2 = 0 + 24.5 Reorder the terms: -24.5 + 24.5 + 2a + a2 = 0 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + 2a + a2 = 0 + 24.5 2a + a2 = 0 + 24.5 Combine like terms: 0 + 24.5 = 24.5 2a + a2 = 24.5 The a term is 2a. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2a + 1 + a2 = 24.5 + 1 Reorder the terms: 1 + 2a + a2 = 24.5 + 1 Combine like terms: 24.5 + 1 = 25.5 1 + 2a + a2 = 25.5 Factor a perfect square on the left side: (a + 1)(a + 1) = 25.5 Calculate the square root of the right side: 5.049752469 Break this problem into two subproblems by setting (a + 1) equal to 5.049752469 and -5.049752469.Subproblem 1
a + 1 = 5.049752469 Simplifying a + 1 = 5.049752469 Reorder the terms: 1 + a = 5.049752469 Solving 1 + a = 5.049752469 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = 5.049752469 + -1 Combine like terms: 1 + -1 = 0 0 + a = 5.049752469 + -1 a = 5.049752469 + -1 Combine like terms: 5.049752469 + -1 = 4.049752469 a = 4.049752469 Simplifying a = 4.049752469Subproblem 2
a + 1 = -5.049752469 Simplifying a + 1 = -5.049752469 Reorder the terms: 1 + a = -5.049752469 Solving 1 + a = -5.049752469 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = -5.049752469 + -1 Combine like terms: 1 + -1 = 0 0 + a = -5.049752469 + -1 a = -5.049752469 + -1 Combine like terms: -5.049752469 + -1 = -6.049752469 a = -6.049752469 Simplifying a = -6.049752469Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.049752469, -6.049752469}Solution
a = {4.049752469, -6.049752469}
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