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Simplifying 16t2 + 128t + 144 = 0 Reorder the terms: 144 + 128t + 16t2 = 0 Solving 144 + 128t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16'. 16(9 + 8t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(9 + 8t + t2)' equal to zero and attempt to solve: Simplifying 9 + 8t + t2 = 0 Solving 9 + 8t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 8t + -9 + t2 = 0 + -9 Reorder the terms: 9 + -9 + 8t + t2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 8t + t2 = 0 + -9 8t + t2 = 0 + -9 Combine like terms: 0 + -9 = -9 8t + t2 = -9 The t term is 8t. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8t + 16 + t2 = -9 + 16 Reorder the terms: 16 + 8t + t2 = -9 + 16 Combine like terms: -9 + 16 = 7 16 + 8t + t2 = 7 Factor a perfect square on the left side: (t + 4)(t + 4) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (t + 4) equal to 2.645751311 and -2.645751311.Subproblem 1
t + 4 = 2.645751311 Simplifying t + 4 = 2.645751311 Reorder the terms: 4 + t = 2.645751311 Solving 4 + t = 2.645751311 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + t = 2.645751311 + -4 Combine like terms: 4 + -4 = 0 0 + t = 2.645751311 + -4 t = 2.645751311 + -4 Combine like terms: 2.645751311 + -4 = -1.354248689 t = -1.354248689 Simplifying t = -1.354248689Subproblem 2
t + 4 = -2.645751311 Simplifying t + 4 = -2.645751311 Reorder the terms: 4 + t = -2.645751311 Solving 4 + t = -2.645751311 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + t = -2.645751311 + -4 Combine like terms: 4 + -4 = 0 0 + t = -2.645751311 + -4 t = -2.645751311 + -4 Combine like terms: -2.645751311 + -4 = -6.645751311 t = -6.645751311 Simplifying t = -6.645751311Solution
The solution to the problem is based on the solutions from the subproblems. t = {-1.354248689, -6.645751311}Solution
t = {-1.354248689, -6.645751311}
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