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Simplifying 48a4 + -252a2 + 49 = 0 Reorder the terms: 49 + -252a2 + 48a4 = 0 Solving 49 + -252a2 + 48a4 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 48 the coefficient of the squared term: Divide each side by '48'. 1.020833333 + -5.25a2 + a4 = 0 Move the constant term to the right: Add '-1.020833333' to each side of the equation. 1.020833333 + -5.25a2 + -1.020833333 + a4 = 0 + -1.020833333 Reorder the terms: 1.020833333 + -1.020833333 + -5.25a2 + a4 = 0 + -1.020833333 Combine like terms: 1.020833333 + -1.020833333 = 0.000000000 0.000000000 + -5.25a2 + a4 = 0 + -1.020833333 -5.25a2 + a4 = 0 + -1.020833333 Combine like terms: 0 + -1.020833333 = -1.020833333 -5.25a2 + a4 = -1.020833333 The a term is -5.25a2. Take half its coefficient (-2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. -5.25a2 + 6.890625 + a4 = -1.020833333 + 6.890625 Reorder the terms: 6.890625 + -5.25a2 + a4 = -1.020833333 + 6.890625 Combine like terms: -1.020833333 + 6.890625 = 5.869791667 6.890625 + -5.25a2 + a4 = 5.869791667 Factor a perfect square on the left side: (a2 + -2.625)(a2 + -2.625) = 5.869791667 Calculate the square root of the right side: 2.422765293 Break this problem into two subproblems by setting (a2 + -2.625) equal to 2.422765293 and -2.422765293.Subproblem 1
a2 + -2.625 = 2.422765293 Simplifying a2 + -2.625 = 2.422765293 Reorder the terms: -2.625 + a2 = 2.422765293 Solving -2.625 + a2 = 2.422765293 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + a2 = 2.422765293 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + a2 = 2.422765293 + 2.625 a2 = 2.422765293 + 2.625 Combine like terms: 2.422765293 + 2.625 = 5.047765293 a2 = 5.047765293 Simplifying a2 = 5.047765293 Take the square root of each side: a = {-2.246723235, 2.246723235}Subproblem 2
a2 + -2.625 = -2.422765293 Simplifying a2 + -2.625 = -2.422765293 Reorder the terms: -2.625 + a2 = -2.422765293 Solving -2.625 + a2 = -2.422765293 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + a2 = -2.422765293 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + a2 = -2.422765293 + 2.625 a2 = -2.422765293 + 2.625 Combine like terms: -2.422765293 + 2.625 = 0.202234707 a2 = 0.202234707 Simplifying a2 = 0.202234707 Take the square root of each side: a = {-0.449705133, 0.449705133}Solution
The solution to the problem is based on the solutions from the subproblems. a = {-2.246723235, 2.246723235, -0.449705133, 0.449705133}
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