0=-t^4+9t^2+400

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Solution for 0=-t^4+9t^2+400 equation:


Simplifying
0 = -1t4 + 9t2 + 400

Reorder the terms:
0 = 400 + 9t2 + -1t4

Solving
0 = 400 + 9t2 + -1t4

Solving for variable 't'.

Combine like terms: 0 + -400 = -400
-400 + -9t2 + t4 = 400 + 9t2 + -1t4 + -400 + -9t2 + t4

Reorder the terms:
-400 + -9t2 + t4 = 400 + -400 + 9t2 + -9t2 + -1t4 + t4

Combine like terms: 400 + -400 = 0
-400 + -9t2 + t4 = 0 + 9t2 + -9t2 + -1t4 + t4
-400 + -9t2 + t4 = 9t2 + -9t2 + -1t4 + t4

Combine like terms: 9t2 + -9t2 = 0
-400 + -9t2 + t4 = 0 + -1t4 + t4
-400 + -9t2 + t4 = -1t4 + t4

Combine like terms: -1t4 + t4 = 0
-400 + -9t2 + t4 = 0

Factor a trinomial.
(-16 + -1t2)(25 + -1t2) = 0

Factor a difference between two squares.
(-16 + -1t2)((5 + t)(5 + -1t)) = 0

Subproblem 1

Set the factor '(-16 + -1t2)' equal to zero and attempt to solve: Simplifying -16 + -1t2 = 0 Solving -16 + -1t2 = 0 Move all terms containing t to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + -1t2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -1t2 = 0 + 16 -1t2 = 0 + 16 Combine like terms: 0 + 16 = 16 -1t2 = 16 Divide each side by '-1'. t2 = -16 Simplifying t2 = -16 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(5 + t)' equal to zero and attempt to solve: Simplifying 5 + t = 0 Solving 5 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + t = 0 + -5 t = 0 + -5 Combine like terms: 0 + -5 = -5 t = -5 Simplifying t = -5

Subproblem 3

Set the factor '(5 + -1t)' equal to zero and attempt to solve: Simplifying 5 + -1t = 0 Solving 5 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1t = 0 + -5 -1t = 0 + -5 Combine like terms: 0 + -5 = -5 -1t = -5 Divide each side by '-1'. t = 5 Simplifying t = 5

Solution

t = {-5, 5}

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