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Simplifying -16t2 + -80t + -21 = 0 Reorder the terms: -21 + -80t + -16t2 = 0 Solving -21 + -80t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '-1'. -1(21 + 80t + 16t2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(21 + 80t + 16t2)' equal to zero and attempt to solve: Simplifying 21 + 80t + 16t2 = 0 Solving 21 + 80t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 1.3125 + 5t + t2 = 0 Move the constant term to the right: Add '-1.3125' to each side of the equation. 1.3125 + 5t + -1.3125 + t2 = 0 + -1.3125 Reorder the terms: 1.3125 + -1.3125 + 5t + t2 = 0 + -1.3125 Combine like terms: 1.3125 + -1.3125 = 0.0000 0.0000 + 5t + t2 = 0 + -1.3125 5t + t2 = 0 + -1.3125 Combine like terms: 0 + -1.3125 = -1.3125 5t + t2 = -1.3125 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 = -1.3125 + 6.25 Reorder the terms: 6.25 + 5t + t2 = -1.3125 + 6.25 Combine like terms: -1.3125 + 6.25 = 4.9375 6.25 + 5t + t2 = 4.9375 Factor a perfect square on the left side: (t + 2.5)(t + 2.5) = 4.9375 Calculate the square root of the right side: 2.222048604 Break this problem into two subproblems by setting (t + 2.5) equal to 2.222048604 and -2.222048604.Subproblem 1
t + 2.5 = 2.222048604 Simplifying t + 2.5 = 2.222048604 Reorder the terms: 2.5 + t = 2.222048604 Solving 2.5 + t = 2.222048604 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 = 2.222048604 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + t = 2.222048604 + -2.5 t = 2.222048604 + -2.5 Combine like terms: 2.222048604 + -2.5 = -0.277951396 t = -0.277951396 Simplifying t = -0.277951396Subproblem 2
t + 2.5 = -2.222048604 Simplifying t + 2.5 = -2.222048604 Reorder the terms: 2.5 + t = -2.222048604 Solving 2.5 + t = -2.222048604 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 = -2.222048604 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + t = -2.222048604 + -2.5 t = -2.222048604 + -2.5 Combine like terms: -2.222048604 + -2.5 = -4.722048604 t = -4.722048604 Simplifying t = -4.722048604Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.277951396, -4.722048604}Solution
t = {-0.277951396, -4.722048604}
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