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Simplifying 126 = -16t2 + 96t Reorder the terms: 126 = 96t + -16t2 Solving 126 = 96t + -16t2 Solving for variable 't'. Reorder the terms: 126 + -96t + 16t2 = 96t + -96t + -16t2 + 16t2 Combine like terms: 96t + -96t = 0 126 + -96t + 16t2 = 0 + -16t2 + 16t2 126 + -96t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 126 + -96t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(63 + -48t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(63 + -48t + 8t2)' equal to zero and attempt to solve: Simplifying 63 + -48t + 8t2 = 0 Solving 63 + -48t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 7.875 + -6t + t2 = 0 Move the constant term to the right: Add '-7.875' to each side of the equation. 7.875 + -6t + -7.875 + t2 = 0 + -7.875 Reorder the terms: 7.875 + -7.875 + -6t + t2 = 0 + -7.875 Combine like terms: 7.875 + -7.875 = 0.000 0.000 + -6t + t2 = 0 + -7.875 -6t + t2 = 0 + -7.875 Combine like terms: 0 + -7.875 = -7.875 -6t + t2 = -7.875 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 = -7.875 + 9 Reorder the terms: 9 + -6t + t2 = -7.875 + 9 Combine like terms: -7.875 + 9 = 1.125 9 + -6t + t2 = 1.125 Factor a perfect square on the left side: (t + -3)(t + -3) = 1.125 Calculate the square root of the right side: 1.060660172 Break this problem into two subproblems by setting (t + -3) equal to 1.060660172 and -1.060660172.Subproblem 1
t + -3 = 1.060660172 Simplifying t + -3 = 1.060660172 Reorder the terms: -3 + t = 1.060660172 Solving -3 + t = 1.060660172 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 = 1.060660172 + 3 Combine like terms: -3 + 3 = 0 0 + t = 1.060660172 + 3 t = 1.060660172 + 3 Combine like terms: 1.060660172 + 3 = 4.060660172 t = 4.060660172 Simplifying t = 4.060660172Subproblem 2
t + -3 = -1.060660172 Simplifying t + -3 = -1.060660172 Reorder the terms: -3 + t = -1.060660172 Solving -3 + t = -1.060660172 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 = -1.060660172 + 3 Combine like terms: -3 + 3 = 0 0 + t = -1.060660172 + 3 t = -1.060660172 + 3 Combine like terms: -1.060660172 + 3 = 1.939339828 t = 1.939339828 Simplifying t = 1.939339828Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.060660172, 1.939339828}Solution
t = {4.060660172, 1.939339828}
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