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Simplifying 4t2 + -24t + 24 = 0 Reorder the terms: 24 + -24t + 4t2 = 0 Solving 24 + -24t + 4t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(6 + -6t + t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(6 + -6t + t2)' equal to zero and attempt to solve: Simplifying 6 + -6t + t2 = 0 Solving 6 + -6t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -6t + -6 + t2 = 0 + -6 Reorder the terms: 6 + -6 + -6t + t2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -6t + t2 = 0 + -6 -6t + t2 = 0 + -6 Combine like terms: 0 + -6 = -6 -6t + t2 = -6 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 = -6 + 9 Reorder the terms: 9 + -6t + t2 = -6 + 9 Combine like terms: -6 + 9 = 3 9 + -6t + t2 = 3 Factor a perfect square on the left side: (t + -3)(t + -3) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (t + -3) equal to 1.732050808 and -1.732050808.Subproblem 1
t + -3 = 1.732050808 Simplifying t + -3 = 1.732050808 Reorder the terms: -3 + t = 1.732050808 Solving -3 + t = 1.732050808 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 = 1.732050808 + 3 Combine like terms: -3 + 3 = 0 0 + t = 1.732050808 + 3 t = 1.732050808 + 3 Combine like terms: 1.732050808 + 3 = 4.732050808 t = 4.732050808 Simplifying t = 4.732050808Subproblem 2
t + -3 = -1.732050808 Simplifying t + -3 = -1.732050808 Reorder the terms: -3 + t = -1.732050808 Solving -3 + t = -1.732050808 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 = -1.732050808 + 3 Combine like terms: -3 + 3 = 0 0 + t = -1.732050808 + 3 t = -1.732050808 + 3 Combine like terms: -1.732050808 + 3 = 1.267949192 t = 1.267949192 Simplifying t = 1.267949192Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.732050808, 1.267949192}Solution
t = {4.732050808, 1.267949192}
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