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Simplifying 50(a2) + -1(a4) + -25 = 0 Reorder the terms: -25 + 50a2 + -1a4 = 0 Solving -25 + 50a2 + -1a4 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 25 + -50a2 + a4 = 0 Move the constant term to the right: Add '-25' to each side of the equation. 25 + -50a2 + -25 + a4 = 0 + -25 Reorder the terms: 25 + -25 + -50a2 + a4 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -50a2 + a4 = 0 + -25 -50a2 + a4 = 0 + -25 Combine like terms: 0 + -25 = -25 -50a2 + a4 = -25 The a term is -50a2. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50a2 + 625 + a4 = -25 + 625 Reorder the terms: 625 + -50a2 + a4 = -25 + 625 Combine like terms: -25 + 625 = 600 625 + -50a2 + a4 = 600 Factor a perfect square on the left side: (a2 + -25)(a2 + -25) = 600 Calculate the square root of the right side: 24.494897428 Break this problem into two subproblems by setting (a2 + -25) equal to 24.494897428 and -24.494897428.Subproblem 1
a2 + -25 = 24.494897428 Simplifying a2 + -25 = 24.494897428 Reorder the terms: -25 + a2 = 24.494897428 Solving -25 + a2 = 24.494897428 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + a2 = 24.494897428 + 25 Combine like terms: -25 + 25 = 0 0 + a2 = 24.494897428 + 25 a2 = 24.494897428 + 25 Combine like terms: 24.494897428 + 25 = 49.494897428 a2 = 49.494897428 Simplifying a2 = 49.494897428 Take the square root of each side: a = {-7.035261006, 7.035261006}Subproblem 2
a2 + -25 = -24.494897428 Simplifying a2 + -25 = -24.494897428 Reorder the terms: -25 + a2 = -24.494897428 Solving -25 + a2 = -24.494897428 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + a2 = -24.494897428 + 25 Combine like terms: -25 + 25 = 0 0 + a2 = -24.494897428 + 25 a2 = -24.494897428 + 25 Combine like terms: -24.494897428 + 25 = 0.505102572 a2 = 0.505102572 Simplifying a2 = 0.505102572 Take the square root of each side: a = {-0.710705686, 0.710705686}Solution
The solution to the problem is based on the solutions from the subproblems. a = {-7.035261006, 7.035261006, -0.710705686, 0.710705686}
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