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Simplifying t4 + 4t2 + -1 = 0 Reorder the terms: -1 + 4t2 + t4 = 0 Solving -1 + 4t2 + t4 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 4t2 + 1 + t4 = 0 + 1 Reorder the terms: -1 + 1 + 4t2 + t4 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 4t2 + t4 = 0 + 1 4t2 + t4 = 0 + 1 Combine like terms: 0 + 1 = 1 4t2 + t4 = 1 The t term is 4t2. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4t2 + 4 + t4 = 1 + 4 Reorder the terms: 4 + 4t2 + t4 = 1 + 4 Combine like terms: 1 + 4 = 5 4 + 4t2 + t4 = 5 Factor a perfect square on the left side: (t2 + 2)(t2 + 2) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (t2 + 2) equal to 2.236067978 and -2.236067978.Subproblem 1
t2 + 2 = 2.236067978 Simplifying t2 + 2 = 2.236067978 Reorder the terms: 2 + t2 = 2.236067978 Solving 2 + t2 = 2.236067978 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + t2 = 2.236067978 + -2 Combine like terms: 2 + -2 = 0 0 + t2 = 2.236067978 + -2 t2 = 2.236067978 + -2 Combine like terms: 2.236067978 + -2 = 0.236067978 t2 = 0.236067978 Simplifying t2 = 0.236067978 Take the square root of each side: t = {-0.485868272, 0.485868272}Subproblem 2
t2 + 2 = -2.236067978 Simplifying t2 + 2 = -2.236067978 Reorder the terms: 2 + t2 = -2.236067978 Solving 2 + t2 = -2.236067978 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + t2 = -2.236067978 + -2 Combine like terms: 2 + -2 = 0 0 + t2 = -2.236067978 + -2 t2 = -2.236067978 + -2 Combine like terms: -2.236067978 + -2 = -4.236067978 t2 = -4.236067978 Simplifying t2 = -4.236067978 Reorder the terms: 4.236067978 + t2 = -4.236067978 + 4.236067978 Combine like terms: -4.236067978 + 4.236067978 = 0.000000000 4.236067978 + 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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