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Simplifying t4 + -12t3 + 16t2 = 0 Reorder the terms: 16t2 + -12t3 + t4 = 0 Solving 16t2 + -12t3 + t4 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't2'. t2(16 + -12t + t2) = 0Subproblem 1
Set the factor 't2' equal to zero and attempt to solve: Simplifying t2 = 0 Solving t2 = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t2 = 0 Take the square root of each side: t = {0}Subproblem 2
Set the factor '(16 + -12t + t2)' equal to zero and attempt to solve: Simplifying 16 + -12t + t2 = 0 Solving 16 + -12t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + -12t + -16 + t2 = 0 + -16 Reorder the terms: 16 + -16 + -12t + t2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -12t + t2 = 0 + -16 -12t + t2 = 0 + -16 Combine like terms: 0 + -16 = -16 -12t + t2 = -16 The t term is -12t. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12t + 36 + t2 = -16 + 36 Reorder the terms: 36 + -12t + t2 = -16 + 36 Combine like terms: -16 + 36 = 20 36 + -12t + t2 = 20 Factor a perfect square on the left side: (t + -6)(t + -6) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (t + -6) equal to 4.472135955 and -4.472135955.Subproblem 1
t + -6 = 4.472135955 Simplifying t + -6 = 4.472135955 Reorder the terms: -6 + t = 4.472135955 Solving -6 + t = 4.472135955 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + t = 4.472135955 + 6 Combine like terms: -6 + 6 = 0 0 + t = 4.472135955 + 6 t = 4.472135955 + 6 Combine like terms: 4.472135955 + 6 = 10.472135955 t = 10.472135955 Simplifying t = 10.472135955Subproblem 2
t + -6 = -4.472135955 Simplifying t + -6 = -4.472135955 Reorder the terms: -6 + t = -4.472135955 Solving -6 + t = -4.472135955 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + t = -4.472135955 + 6 Combine like terms: -6 + 6 = 0 0 + t = -4.472135955 + 6 t = -4.472135955 + 6 Combine like terms: -4.472135955 + 6 = 1.527864045 t = 1.527864045 Simplifying t = 1.527864045Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.472135955, 1.527864045}Solution
t = {0, 10.472135955, 1.527864045}
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