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Simplifying t3 + -30t2 + -100t = 0 Reorder the terms: -100t + -30t2 + t3 = 0 Solving -100t + -30t2 + t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(-100 + -30t + 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 '(-100 + -30t + t2)' equal to zero and attempt to solve: Simplifying -100 + -30t + t2 = 0 Solving -100 + -30t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + -30t + 100 + t2 = 0 + 100 Reorder the terms: -100 + 100 + -30t + t2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -30t + t2 = 0 + 100 -30t + t2 = 0 + 100 Combine like terms: 0 + 100 = 100 -30t + t2 = 100 The t term is -30t. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30t + 225 + t2 = 100 + 225 Reorder the terms: 225 + -30t + t2 = 100 + 225 Combine like terms: 100 + 225 = 325 225 + -30t + t2 = 325 Factor a perfect square on the left side: (t + -15)(t + -15) = 325 Calculate the square root of the right side: 18.027756377 Break this problem into two subproblems by setting (t + -15) equal to 18.027756377 and -18.027756377.Subproblem 1
t + -15 = 18.027756377 Simplifying t + -15 = 18.027756377 Reorder the terms: -15 + t = 18.027756377 Solving -15 + t = 18.027756377 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + t = 18.027756377 + 15 Combine like terms: -15 + 15 = 0 0 + t = 18.027756377 + 15 t = 18.027756377 + 15 Combine like terms: 18.027756377 + 15 = 33.027756377 t = 33.027756377 Simplifying t = 33.027756377Subproblem 2
t + -15 = -18.027756377 Simplifying t + -15 = -18.027756377 Reorder the terms: -15 + t = -18.027756377 Solving -15 + t = -18.027756377 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + t = -18.027756377 + 15 Combine like terms: -15 + 15 = 0 0 + t = -18.027756377 + 15 t = -18.027756377 + 15 Combine like terms: -18.027756377 + 15 = -3.027756377 t = -3.027756377 Simplifying t = -3.027756377Solution
The solution to the problem is based on the solutions from the subproblems. t = {33.027756377, -3.027756377}Solution
t = {0, 33.027756377, -3.027756377}
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