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Simplifying t4 + 20t2 + -24 = 0 Reorder the terms: -24 + 20t2 + t4 = 0 Solving -24 + 20t2 + t4 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + 20t2 + 24 + t4 = 0 + 24 Reorder the terms: -24 + 24 + 20t2 + t4 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 20t2 + t4 = 0 + 24 20t2 + t4 = 0 + 24 Combine like terms: 0 + 24 = 24 20t2 + t4 = 24 The t term is 20t2. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20t2 + 100 + t4 = 24 + 100 Reorder the terms: 100 + 20t2 + t4 = 24 + 100 Combine like terms: 24 + 100 = 124 100 + 20t2 + t4 = 124 Factor a perfect square on the left side: (t2 + 10)(t2 + 10) = 124 Calculate the square root of the right side: 11.135528726 Break this problem into two subproblems by setting (t2 + 10) equal to 11.135528726 and -11.135528726.Subproblem 1
t2 + 10 = 11.135528726 Simplifying t2 + 10 = 11.135528726 Reorder the terms: 10 + t2 = 11.135528726 Solving 10 + t2 = 11.135528726 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + t2 = 11.135528726 + -10 Combine like terms: 10 + -10 = 0 0 + t2 = 11.135528726 + -10 t2 = 11.135528726 + -10 Combine like terms: 11.135528726 + -10 = 1.135528726 t2 = 1.135528726 Simplifying t2 = 1.135528726 Take the square root of each side: t = {-1.065611902, 1.065611902}Subproblem 2
t2 + 10 = -11.135528726 Simplifying t2 + 10 = -11.135528726 Reorder the terms: 10 + t2 = -11.135528726 Solving 10 + t2 = -11.135528726 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + t2 = -11.135528726 + -10 Combine like terms: 10 + -10 = 0 0 + t2 = -11.135528726 + -10 t2 = -11.135528726 + -10 Combine like terms: -11.135528726 + -10 = -21.135528726 t2 = -21.135528726 Simplifying t2 = -21.135528726 Reorder the terms: 21.135528726 + t2 = -21.135528726 + 21.135528726 Combine like terms: -21.135528726 + 21.135528726 = 0.000000000 21.135528726 + 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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