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Simplifying 16t2 + 176t = 448 Reorder the terms: 176t + 16t2 = 448 Solving 176t + 16t2 = 448 Solving for variable 't'. Reorder the terms: -448 + 176t + 16t2 = 448 + -448 Combine like terms: 448 + -448 = 0 -448 + 176t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-28 + 11t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-28 + 11t + t2)' equal to zero and attempt to solve: Simplifying -28 + 11t + t2 = 0 Solving -28 + 11t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + 11t + 28 + t2 = 0 + 28 Reorder the terms: -28 + 28 + 11t + t2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 11t + t2 = 0 + 28 11t + t2 = 0 + 28 Combine like terms: 0 + 28 = 28 11t + t2 = 28 The t term is 11t. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11t + 30.25 + t2 = 28 + 30.25 Reorder the terms: 30.25 + 11t + t2 = 28 + 30.25 Combine like terms: 28 + 30.25 = 58.25 30.25 + 11t + t2 = 58.25 Factor a perfect square on the left side: (t + 5.5)(t + 5.5) = 58.25 Calculate the square root of the right side: 7.632168761 Break this problem into two subproblems by setting (t + 5.5) equal to 7.632168761 and -7.632168761.Subproblem 1
t + 5.5 = 7.632168761 Simplifying t + 5.5 = 7.632168761 Reorder the terms: 5.5 + t = 7.632168761 Solving 5.5 + t = 7.632168761 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + t = 7.632168761 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + t = 7.632168761 + -5.5 t = 7.632168761 + -5.5 Combine like terms: 7.632168761 + -5.5 = 2.132168761 t = 2.132168761 Simplifying t = 2.132168761Subproblem 2
t + 5.5 = -7.632168761 Simplifying t + 5.5 = -7.632168761 Reorder the terms: 5.5 + t = -7.632168761 Solving 5.5 + t = -7.632168761 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + t = -7.632168761 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + t = -7.632168761 + -5.5 t = -7.632168761 + -5.5 Combine like terms: -7.632168761 + -5.5 = -13.132168761 t = -13.132168761 Simplifying t = -13.132168761Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.132168761, -13.132168761}Solution
t = {2.132168761, -13.132168761}
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