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Simplifying 50t2 + -1t4 + 4000 = 0 Reorder the terms: 4000 + 50t2 + -1t4 = 0 Solving 4000 + 50t2 + -1t4 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4000 + -50t2 + t4 = 0 Move the constant term to the right: Add '4000' to each side of the equation. -4000 + -50t2 + 4000 + t4 = 0 + 4000 Reorder the terms: -4000 + 4000 + -50t2 + t4 = 0 + 4000 Combine like terms: -4000 + 4000 = 0 0 + -50t2 + t4 = 0 + 4000 -50t2 + t4 = 0 + 4000 Combine like terms: 0 + 4000 = 4000 -50t2 + t4 = 4000 The t term is -50t2. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50t2 + 625 + t4 = 4000 + 625 Reorder the terms: 625 + -50t2 + t4 = 4000 + 625 Combine like terms: 4000 + 625 = 4625 625 + -50t2 + t4 = 4625 Factor a perfect square on the left side: (t2 + -25)(t2 + -25) = 4625 Calculate the square root of the right side: 68.007352544 Break this problem into two subproblems by setting (t2 + -25) equal to 68.007352544 and -68.007352544.Subproblem 1
t2 + -25 = 68.007352544 Simplifying t2 + -25 = 68.007352544 Reorder the terms: -25 + t2 = 68.007352544 Solving -25 + t2 = 68.007352544 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + t2 = 68.007352544 + 25 Combine like terms: -25 + 25 = 0 0 + t2 = 68.007352544 + 25 t2 = 68.007352544 + 25 Combine like terms: 68.007352544 + 25 = 93.007352544 t2 = 93.007352544 Simplifying t2 = 93.007352544 Take the square root of each side: t = {-9.644031965, 9.644031965}Subproblem 2
t2 + -25 = -68.007352544 Simplifying t2 + -25 = -68.007352544 Reorder the terms: -25 + t2 = -68.007352544 Solving -25 + t2 = -68.007352544 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + t2 = -68.007352544 + 25 Combine like terms: -25 + 25 = 0 0 + t2 = -68.007352544 + 25 t2 = -68.007352544 + 25 Combine like terms: -68.007352544 + 25 = -43.007352544 t2 = -43.007352544 Simplifying t2 = -43.007352544 Reorder the terms: 43.007352544 + t2 = -43.007352544 + 43.007352544 Combine like terms: -43.007352544 + 43.007352544 = 0.000000000 43.007352544 + t2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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