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Simplifying 16t2 + 80t + 4 = 0 Reorder the terms: 4 + 80t + 16t2 = 0 Solving 4 + 80t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(1 + 20t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + 20t + 4t2)' equal to zero and attempt to solve: Simplifying 1 + 20t + 4t2 = 0 Solving 1 + 20t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.25 + 5t + t2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 5t + -0.25 + t2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 5t + t2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 5t + t2 = 0 + -0.25 5t + t2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 5t + t2 = -0.25 The t term is 5t. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5t + 6.25 + t2 = -0.25 + 6.25 Reorder the terms: 6.25 + 5t + t2 = -0.25 + 6.25 Combine like terms: -0.25 + 6.25 = 6 6.25 + 5t + t2 = 6 Factor a perfect square on the left side: (t + 2.5)(t + 2.5) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (t + 2.5) equal to 2.449489743 and -2.449489743.Subproblem 1
t + 2.5 = 2.449489743 Simplifying t + 2.5 = 2.449489743 Reorder the terms: 2.5 + t = 2.449489743 Solving 2.5 + t = 2.449489743 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + t = 2.449489743 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + t = 2.449489743 + -2.5 t = 2.449489743 + -2.5 Combine like terms: 2.449489743 + -2.5 = -0.050510257 t = -0.050510257 Simplifying t = -0.050510257Subproblem 2
t + 2.5 = -2.449489743 Simplifying t + 2.5 = -2.449489743 Reorder the terms: 2.5 + t = -2.449489743 Solving 2.5 + t = -2.449489743 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + t = -2.449489743 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + t = -2.449489743 + -2.5 t = -2.449489743 + -2.5 Combine like terms: -2.449489743 + -2.5 = -4.949489743 t = -4.949489743 Simplifying t = -4.949489743Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.050510257, -4.949489743}Solution
t = {-0.050510257, -4.949489743}
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