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Simplifying t3 + -5t2 + 9t = 0 Reorder the terms: 9t + -5t2 + t3 = 0 Solving 9t + -5t2 + t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(9 + -5t + 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 '(9 + -5t + t2)' equal to zero and attempt to solve: Simplifying 9 + -5t + t2 = 0 Solving 9 + -5t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -5t + -9 + t2 = 0 + -9 Reorder the terms: 9 + -9 + -5t + t2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -5t + t2 = 0 + -9 -5t + t2 = 0 + -9 Combine like terms: 0 + -9 = -9 -5t + t2 = -9 The t term is -5t. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5t + 6.25 + t2 = -9 + 6.25 Reorder the terms: 6.25 + -5t + t2 = -9 + 6.25 Combine like terms: -9 + 6.25 = -2.75 6.25 + -5t + t2 = -2.75 Factor a perfect square on the left side: (t + -2.5)(t + -2.5) = -2.75 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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