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Simplifying t3 + -6t2 + 19t = 0 Reorder the terms: 19t + -6t2 + t3 = 0 Solving 19t + -6t2 + t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(19 + -6t + 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 '(19 + -6t + t2)' equal to zero and attempt to solve: Simplifying 19 + -6t + t2 = 0 Solving 19 + -6t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-19' to each side of the equation. 19 + -6t + -19 + t2 = 0 + -19 Reorder the terms: 19 + -19 + -6t + t2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -6t + t2 = 0 + -19 -6t + t2 = 0 + -19 Combine like terms: 0 + -19 = -19 -6t + t2 = -19 The t term is -6t. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6t + 9 + t2 = -19 + 9 Reorder the terms: 9 + -6t + t2 = -19 + 9 Combine like terms: -19 + 9 = -10 9 + -6t + t2 = -10 Factor a perfect square on the left side: (t + -3)(t + -3) = -10 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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