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Simplifying 5 = 16t2 + 64t + 5 Reorder the terms: 5 = 5 + 64t + 16t2 Add '-5' to each side of the equation. 5 + -5 = 5 + 64t + -5 + 16t2 Combine like terms: 5 + -5 = 0 0 = 5 + 64t + -5 + 16t2 Reorder the terms: 0 = 5 + -5 + 64t + 16t2 Combine like terms: 5 + -5 = 0 0 = 0 + 64t + 16t2 0 = 64t + 16t2 Solving 0 = 64t + 16t2 Solving for variable 't'. Remove the zero: -64t + -16t2 = 64t + 16t2 + -64t + -16t2 Reorder the terms: -64t + -16t2 = 64t + -64t + 16t2 + -16t2 Combine like terms: 64t + -64t = 0 -64t + -16t2 = 0 + 16t2 + -16t2 -64t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -64t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-16t'. -16t(4 + t) = 0 Ignore the factor -16.Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
Set the factor '(4 + t)' equal to zero and attempt to solve: Simplifying 4 + t = 0 Solving 4 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + t = 0 + -4 t = 0 + -4 Combine like terms: 0 + -4 = -4 t = -4 Simplifying t = -4Solution
t = {0, -4}
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