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Simplifying 0 = -16t2 + 205t + 10 Reorder the terms: 0 = 10 + 205t + -16t2 Solving 0 = 10 + 205t + -16t2 Solving for variable 't'. Combine like terms: 0 + -10 = -10 -10 + -205t + 16t2 = 10 + 205t + -16t2 + -10 + -205t + 16t2 Reorder the terms: -10 + -205t + 16t2 = 10 + -10 + 205t + -205t + -16t2 + 16t2 Combine like terms: 10 + -10 = 0 -10 + -205t + 16t2 = 0 + 205t + -205t + -16t2 + 16t2 -10 + -205t + 16t2 = 205t + -205t + -16t2 + 16t2 Combine like terms: 205t + -205t = 0 -10 + -205t + 16t2 = 0 + -16t2 + 16t2 -10 + -205t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -10 + -205t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.625 + -12.8125t + t2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -12.8125t + 0.625 + t2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -12.8125t + t2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -12.8125t + t2 = 0 + 0.625 -12.8125t + t2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -12.8125t + t2 = 0.625 The t term is -12.8125t. Take half its coefficient (-6.40625). Square it (41.04003906) and add it to both sides. Add '41.04003906' to each side of the equation. -12.8125t + 41.04003906 + t2 = 0.625 + 41.04003906 Reorder the terms: 41.04003906 + -12.8125t + t2 = 0.625 + 41.04003906 Combine like terms: 0.625 + 41.04003906 = 41.66503906 41.04003906 + -12.8125t + t2 = 41.66503906 Factor a perfect square on the left side: (t + -6.40625)(t + -6.40625) = 41.66503906 Calculate the square root of the right side: 6.454846169 Break this problem into two subproblems by setting (t + -6.40625) equal to 6.454846169 and -6.454846169.Subproblem 1
t + -6.40625 = 6.454846169 Simplifying t + -6.40625 = 6.454846169 Reorder the terms: -6.40625 + t = 6.454846169 Solving -6.40625 + t = 6.454846169 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.40625' to each side of the equation. -6.40625 + 6.40625 + t = 6.454846169 + 6.40625 Combine like terms: -6.40625 + 6.40625 = 0.00000 0.00000 + t = 6.454846169 + 6.40625 t = 6.454846169 + 6.40625 Combine like terms: 6.454846169 + 6.40625 = 12.861096169 t = 12.861096169 Simplifying t = 12.861096169Subproblem 2
t + -6.40625 = -6.454846169 Simplifying t + -6.40625 = -6.454846169 Reorder the terms: -6.40625 + t = -6.454846169 Solving -6.40625 + t = -6.454846169 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.40625' to each side of the equation. -6.40625 + 6.40625 + t = -6.454846169 + 6.40625 Combine like terms: -6.40625 + 6.40625 = 0.00000 0.00000 + t = -6.454846169 + 6.40625 t = -6.454846169 + 6.40625 Combine like terms: -6.454846169 + 6.40625 = -0.048596169 t = -0.048596169 Simplifying t = -0.048596169Solution
The solution to the problem is based on the solutions from the subproblems. t = {12.861096169, -0.048596169}
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