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Simplifying (t) = -16t2 + 6t + 200 t = -16t2 + 6t + 200 Reorder the terms: t = 200 + 6t + -16t2 Solving t = 200 + 6t + -16t2 Solving for variable 't'. Reorder the terms: -200 + t + -6t + 16t2 = 200 + 6t + -16t2 + -200 + -6t + 16t2 Combine like terms: t + -6t = -5t -200 + -5t + 16t2 = 200 + 6t + -16t2 + -200 + -6t + 16t2 Reorder the terms: -200 + -5t + 16t2 = 200 + -200 + 6t + -6t + -16t2 + 16t2 Combine like terms: 200 + -200 = 0 -200 + -5t + 16t2 = 0 + 6t + -6t + -16t2 + 16t2 -200 + -5t + 16t2 = 6t + -6t + -16t2 + 16t2 Combine like terms: 6t + -6t = 0 -200 + -5t + 16t2 = 0 + -16t2 + 16t2 -200 + -5t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -200 + -5t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -12.5 + -0.3125t + t2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -0.3125t + 12.5 + t2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -0.3125t + t2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -0.3125t + t2 = 0 + 12.5 -0.3125t + t2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -0.3125t + t2 = 12.5 The t term is -0.3125t. Take half its coefficient (-0.15625). Square it (0.0244140625) and add it to both sides. Add '0.0244140625' to each side of the equation. -0.3125t + 0.0244140625 + t2 = 12.5 + 0.0244140625 Reorder the terms: 0.0244140625 + -0.3125t + t2 = 12.5 + 0.0244140625 Combine like terms: 12.5 + 0.0244140625 = 12.5244140625 0.0244140625 + -0.3125t + t2 = 12.5244140625 Factor a perfect square on the left side: (t + -0.15625)(t + -0.15625) = 12.5244140625 Calculate the square root of the right side: 3.538984892 Break this problem into two subproblems by setting (t + -0.15625) equal to 3.538984892 and -3.538984892.Subproblem 1
t + -0.15625 = 3.538984892 Simplifying t + -0.15625 = 3.538984892 Reorder the terms: -0.15625 + t = 3.538984892 Solving -0.15625 + t = 3.538984892 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.15625' to each side of the equation. -0.15625 + 0.15625 + t = 3.538984892 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + t = 3.538984892 + 0.15625 t = 3.538984892 + 0.15625 Combine like terms: 3.538984892 + 0.15625 = 3.695234892 t = 3.695234892 Simplifying t = 3.695234892Subproblem 2
t + -0.15625 = -3.538984892 Simplifying t + -0.15625 = -3.538984892 Reorder the terms: -0.15625 + t = -3.538984892 Solving -0.15625 + t = -3.538984892 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.15625' to each side of the equation. -0.15625 + 0.15625 + t = -3.538984892 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + t = -3.538984892 + 0.15625 t = -3.538984892 + 0.15625 Combine like terms: -3.538984892 + 0.15625 = -3.382734892 t = -3.382734892 Simplifying t = -3.382734892Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.695234892, -3.382734892}
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