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Simplifying -16t2 + -1000t + 1900 = 0 Reorder the terms: 1900 + -1000t + -16t2 = 0 Solving 1900 + -1000t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(475 + -250t + -4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(475 + -250t + -4t2)' equal to zero and attempt to solve: Simplifying 475 + -250t + -4t2 = 0 Solving 475 + -250t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -118.75 + 62.5t + t2 = 0 Move the constant term to the right: Add '118.75' to each side of the equation. -118.75 + 62.5t + 118.75 + t2 = 0 + 118.75 Reorder the terms: -118.75 + 118.75 + 62.5t + t2 = 0 + 118.75 Combine like terms: -118.75 + 118.75 = 0.00 0.00 + 62.5t + t2 = 0 + 118.75 62.5t + t2 = 0 + 118.75 Combine like terms: 0 + 118.75 = 118.75 62.5t + t2 = 118.75 The t term is 62.5t. Take half its coefficient (31.25). Square it (976.5625) and add it to both sides. Add '976.5625' to each side of the equation. 62.5t + 976.5625 + t2 = 118.75 + 976.5625 Reorder the terms: 976.5625 + 62.5t + t2 = 118.75 + 976.5625 Combine like terms: 118.75 + 976.5625 = 1095.3125 976.5625 + 62.5t + t2 = 1095.3125 Factor a perfect square on the left side: (t + 31.25)(t + 31.25) = 1095.3125 Calculate the square root of the right side: 33.095505737 Break this problem into two subproblems by setting (t + 31.25) equal to 33.095505737 and -33.095505737.Subproblem 1
t + 31.25 = 33.095505737 Simplifying t + 31.25 = 33.095505737 Reorder the terms: 31.25 + t = 33.095505737 Solving 31.25 + t = 33.095505737 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-31.25' to each side of the equation. 31.25 + -31.25 + t = 33.095505737 + -31.25 Combine like terms: 31.25 + -31.25 = 0.00 0.00 + t = 33.095505737 + -31.25 t = 33.095505737 + -31.25 Combine like terms: 33.095505737 + -31.25 = 1.845505737 t = 1.845505737 Simplifying t = 1.845505737Subproblem 2
t + 31.25 = -33.095505737 Simplifying t + 31.25 = -33.095505737 Reorder the terms: 31.25 + t = -33.095505737 Solving 31.25 + t = -33.095505737 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-31.25' to each side of the equation. 31.25 + -31.25 + t = -33.095505737 + -31.25 Combine like terms: 31.25 + -31.25 = 0.00 0.00 + t = -33.095505737 + -31.25 t = -33.095505737 + -31.25 Combine like terms: -33.095505737 + -31.25 = -64.345505737 t = -64.345505737 Simplifying t = -64.345505737Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.845505737, -64.345505737}Solution
t = {1.845505737, -64.345505737}
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