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Simplifying t4 + 6t2 + -2 = 0 Reorder the terms: -2 + 6t2 + t4 = 0 Solving -2 + 6t2 + t4 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 6t2 + 2 + t4 = 0 + 2 Reorder the terms: -2 + 2 + 6t2 + t4 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 6t2 + t4 = 0 + 2 6t2 + t4 = 0 + 2 Combine like terms: 0 + 2 = 2 6t2 + t4 = 2 The t term is 6t2. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6t2 + 9 + t4 = 2 + 9 Reorder the terms: 9 + 6t2 + t4 = 2 + 9 Combine like terms: 2 + 9 = 11 9 + 6t2 + t4 = 11 Factor a perfect square on the left side: (t2 + 3)(t2 + 3) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (t2 + 3) equal to 3.31662479 and -3.31662479.Subproblem 1
t2 + 3 = 3.31662479 Simplifying t2 + 3 = 3.31662479 Reorder the terms: 3 + t2 = 3.31662479 Solving 3 + t2 = 3.31662479 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + t2 = 3.31662479 + -3 Combine like terms: 3 + -3 = 0 0 + t2 = 3.31662479 + -3 t2 = 3.31662479 + -3 Combine like terms: 3.31662479 + -3 = 0.31662479 t2 = 0.31662479 Simplifying t2 = 0.31662479 Take the square root of each side: t = {-0.562694224, 0.562694224}Subproblem 2
t2 + 3 = -3.31662479 Simplifying t2 + 3 = -3.31662479 Reorder the terms: 3 + t2 = -3.31662479 Solving 3 + t2 = -3.31662479 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + t2 = -3.31662479 + -3 Combine like terms: 3 + -3 = 0 0 + t2 = -3.31662479 + -3 t2 = -3.31662479 + -3 Combine like terms: -3.31662479 + -3 = -6.31662479 t2 = -6.31662479 Simplifying t2 = -6.31662479 Reorder the terms: 6.31662479 + t2 = -6.31662479 + 6.31662479 Combine like terms: -6.31662479 + 6.31662479 = 0.00000000 6.31662479 + t2 = 0.00000000 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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