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Simplifying t4 + 16.42t2 = 204.55 Reorder the terms: 16.42t2 + t4 = 204.55 Solving 16.42t2 + t4 = 204.55 Solving for variable 't'. Reorder the terms: -204.55 + 16.42t2 + t4 = 204.55 + -204.55 Combine like terms: 204.55 + -204.55 = 0.00 -204.55 + 16.42t2 + t4 = 0.00 Begin completing the square. Move the constant term to the right: Add '204.55' to each side of the equation. -204.55 + 16.42t2 + 204.55 + t4 = 0.00 + 204.55 Reorder the terms: -204.55 + 204.55 + 16.42t2 + t4 = 0.00 + 204.55 Combine like terms: -204.55 + 204.55 = 0.00 0.00 + 16.42t2 + t4 = 0.00 + 204.55 16.42t2 + t4 = 0.00 + 204.55 Combine like terms: 0.00 + 204.55 = 204.55 16.42t2 + t4 = 204.55 The t term is 16.42t2. Take half its coefficient (8.21). Square it (67.4041) and add it to both sides. Add '67.4041' to each side of the equation. 16.42t2 + 67.4041 + t4 = 204.55 + 67.4041 Reorder the terms: 67.4041 + 16.42t2 + t4 = 204.55 + 67.4041 Combine like terms: 204.55 + 67.4041 = 271.9541 67.4041 + 16.42t2 + t4 = 271.9541 Factor a perfect square on the left side: (t2 + 8.21)(t2 + 8.21) = 271.9541 Calculate the square root of the right side: 16.491030896 Break this problem into two subproblems by setting (t2 + 8.21) equal to 16.491030896 and -16.491030896.Subproblem 1
t2 + 8.21 = 16.491030896 Simplifying t2 + 8.21 = 16.491030896 Reorder the terms: 8.21 + t2 = 16.491030896 Solving 8.21 + t2 = 16.491030896 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-8.21' to each side of the equation. 8.21 + -8.21 + t2 = 16.491030896 + -8.21 Combine like terms: 8.21 + -8.21 = 0.00 0.00 + t2 = 16.491030896 + -8.21 t2 = 16.491030896 + -8.21 Combine like terms: 16.491030896 + -8.21 = 8.281030896 t2 = 8.281030896 Simplifying t2 = 8.281030896 Take the square root of each side: t = {-2.877678039, 2.877678039}Subproblem 2
t2 + 8.21 = -16.491030896 Simplifying t2 + 8.21 = -16.491030896 Reorder the terms: 8.21 + t2 = -16.491030896 Solving 8.21 + t2 = -16.491030896 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-8.21' to each side of the equation. 8.21 + -8.21 + t2 = -16.491030896 + -8.21 Combine like terms: 8.21 + -8.21 = 0.00 0.00 + t2 = -16.491030896 + -8.21 t2 = -16.491030896 + -8.21 Combine like terms: -16.491030896 + -8.21 = -24.701030896 t2 = -24.701030896 Simplifying t2 = -24.701030896 Reorder the terms: 24.701030896 + t2 = -24.701030896 + 24.701030896 Combine like terms: -24.701030896 + 24.701030896 = 0.000000000 24.701030896 + 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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