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Simplifying t3 + -8t2 + 22t = 0 Reorder the terms: 22t + -8t2 + t3 = 0 Solving 22t + -8t2 + t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(22 + -8t + t2) = 0Subproblem 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 '(22 + -8t + t2)' equal to zero and attempt to solve: Simplifying 22 + -8t + t2 = 0 Solving 22 + -8t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-22' to each side of the equation. 22 + -8t + -22 + t2 = 0 + -22 Reorder the terms: 22 + -22 + -8t + t2 = 0 + -22 Combine like terms: 22 + -22 = 0 0 + -8t + t2 = 0 + -22 -8t + t2 = 0 + -22 Combine like terms: 0 + -22 = -22 -8t + t2 = -22 The t term is -8t. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8t + 16 + t2 = -22 + 16 Reorder the terms: 16 + -8t + t2 = -22 + 16 Combine like terms: -22 + 16 = -6 16 + -8t + t2 = -6 Factor a perfect square on the left side: (t + -4)(t + -4) = -6 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
t = {0}
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