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Simplifying 4t3 + -24t2 + -36t = 0 Reorder the terms: -36t + -24t2 + 4t3 = 0 Solving -36t + -24t2 + 4t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4t'. 4t(-9 + -6t + t2) = 0 Ignore the factor 4.Subproblem 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 + -6t + t2)' equal to zero and attempt to solve: Simplifying -9 + -6t + t2 = 0 Solving -9 + -6t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -6t + 9 + t2 = 0 + 9 Reorder the terms: -9 + 9 + -6t + t2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -6t + t2 = 0 + 9 -6t + t2 = 0 + 9 Combine like terms: 0 + 9 = 9 -6t + t2 = 9 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 = 9 + 9 Reorder the terms: 9 + -6t + t2 = 9 + 9 Combine like terms: 9 + 9 = 18 9 + -6t + t2 = 18 Factor a perfect square on the left side: (t + -3)(t + -3) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (t + -3) equal to 4.242640687 and -4.242640687.Subproblem 1
t + -3 = 4.242640687 Simplifying t + -3 = 4.242640687 Reorder the terms: -3 + t = 4.242640687 Solving -3 + t = 4.242640687 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = 4.242640687 + 3 Combine like terms: -3 + 3 = 0 0 + t = 4.242640687 + 3 t = 4.242640687 + 3 Combine like terms: 4.242640687 + 3 = 7.242640687 t = 7.242640687 Simplifying t = 7.242640687Subproblem 2
t + -3 = -4.242640687 Simplifying t + -3 = -4.242640687 Reorder the terms: -3 + t = -4.242640687 Solving -3 + t = -4.242640687 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = -4.242640687 + 3 Combine like terms: -3 + 3 = 0 0 + t = -4.242640687 + 3 t = -4.242640687 + 3 Combine like terms: -4.242640687 + 3 = -1.242640687 t = -1.242640687 Simplifying t = -1.242640687Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.242640687, -1.242640687}Solution
t = {0, 7.242640687, -1.242640687}
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