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Simplifying t3 + -33t2 + -10t = 0 Reorder the terms: -10t + -33t2 + t3 = 0 Solving -10t + -33t2 + t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(-10 + -33t + 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 '(-10 + -33t + t2)' equal to zero and attempt to solve: Simplifying -10 + -33t + t2 = 0 Solving -10 + -33t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -33t + 10 + t2 = 0 + 10 Reorder the terms: -10 + 10 + -33t + t2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -33t + t2 = 0 + 10 -33t + t2 = 0 + 10 Combine like terms: 0 + 10 = 10 -33t + t2 = 10 The t term is -33t. Take half its coefficient (-16.5). Square it (272.25) and add it to both sides. Add '272.25' to each side of the equation. -33t + 272.25 + t2 = 10 + 272.25 Reorder the terms: 272.25 + -33t + t2 = 10 + 272.25 Combine like terms: 10 + 272.25 = 282.25 272.25 + -33t + t2 = 282.25 Factor a perfect square on the left side: (t + -16.5)(t + -16.5) = 282.25 Calculate the square root of the right side: 16.800297616 Break this problem into two subproblems by setting (t + -16.5) equal to 16.800297616 and -16.800297616.Subproblem 1
t + -16.5 = 16.800297616 Simplifying t + -16.5 = 16.800297616 Reorder the terms: -16.5 + t = 16.800297616 Solving -16.5 + t = 16.800297616 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '16.5' to each side of the equation. -16.5 + 16.5 + t = 16.800297616 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + t = 16.800297616 + 16.5 t = 16.800297616 + 16.5 Combine like terms: 16.800297616 + 16.5 = 33.300297616 t = 33.300297616 Simplifying t = 33.300297616Subproblem 2
t + -16.5 = -16.800297616 Simplifying t + -16.5 = -16.800297616 Reorder the terms: -16.5 + t = -16.800297616 Solving -16.5 + t = -16.800297616 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '16.5' to each side of the equation. -16.5 + 16.5 + t = -16.800297616 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + t = -16.800297616 + 16.5 t = -16.800297616 + 16.5 Combine like terms: -16.800297616 + 16.5 = -0.300297616 t = -0.300297616 Simplifying t = -0.300297616Solution
The solution to the problem is based on the solutions from the subproblems. t = {33.300297616, -0.300297616}Solution
t = {0, 33.300297616, -0.300297616}
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