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Simplifying 16t2 + 64t = 48 Reorder the terms: 64t + 16t2 = 48 Solving 64t + 16t2 = 48 Solving for variable 't'. Reorder the terms: -48 + 64t + 16t2 = 48 + -48 Combine like terms: 48 + -48 = 0 -48 + 64t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-3 + 4t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-3 + 4t + t2)' equal to zero and attempt to solve: Simplifying -3 + 4t + t2 = 0 Solving -3 + 4t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 4t + 3 + t2 = 0 + 3 Reorder the terms: -3 + 3 + 4t + t2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 4t + t2 = 0 + 3 4t + t2 = 0 + 3 Combine like terms: 0 + 3 = 3 4t + t2 = 3 The t term is 4t. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4t + 4 + t2 = 3 + 4 Reorder the terms: 4 + 4t + t2 = 3 + 4 Combine like terms: 3 + 4 = 7 4 + 4t + t2 = 7 Factor a perfect square on the left side: (t + 2)(t + 2) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (t + 2) equal to 2.645751311 and -2.645751311.Subproblem 1
t + 2 = 2.645751311 Simplifying t + 2 = 2.645751311 Reorder the terms: 2 + t = 2.645751311 Solving 2 + t = 2.645751311 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + t = 2.645751311 + -2 Combine like terms: 2 + -2 = 0 0 + t = 2.645751311 + -2 t = 2.645751311 + -2 Combine like terms: 2.645751311 + -2 = 0.645751311 t = 0.645751311 Simplifying t = 0.645751311Subproblem 2
t + 2 = -2.645751311 Simplifying t + 2 = -2.645751311 Reorder the terms: 2 + t = -2.645751311 Solving 2 + t = -2.645751311 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + t = -2.645751311 + -2 Combine like terms: 2 + -2 = 0 0 + t = -2.645751311 + -2 t = -2.645751311 + -2 Combine like terms: -2.645751311 + -2 = -4.645751311 t = -4.645751311 Simplifying t = -4.645751311Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.645751311, -4.645751311}Solution
t = {0.645751311, -4.645751311}
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