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Simplifying 0 = 4 + 50t + -16t2 Solving 0 = 4 + 50t + -16t2 Solving for variable 't'. Combine like terms: 0 + -4 = -4 -4 + -50t + 16t2 = 4 + 50t + -16t2 + -4 + -50t + 16t2 Reorder the terms: -4 + -50t + 16t2 = 4 + -4 + 50t + -50t + -16t2 + 16t2 Combine like terms: 4 + -4 = 0 -4 + -50t + 16t2 = 0 + 50t + -50t + -16t2 + 16t2 -4 + -50t + 16t2 = 50t + -50t + -16t2 + 16t2 Combine like terms: 50t + -50t = 0 -4 + -50t + 16t2 = 0 + -16t2 + 16t2 -4 + -50t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -4 + -50t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + -25t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -25t + 8t2)' equal to zero and attempt to solve: Simplifying -2 + -25t + 8t2 = 0 Solving -2 + -25t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.25 + -3.125t + t2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -3.125t + 0.25 + t2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -3.125t + t2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -3.125t + t2 = 0 + 0.25 -3.125t + t2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -3.125t + t2 = 0.25 The t term is -3.125t. Take half its coefficient (-1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. -3.125t + 2.44140625 + t2 = 0.25 + 2.44140625 Reorder the terms: 2.44140625 + -3.125t + t2 = 0.25 + 2.44140625 Combine like terms: 0.25 + 2.44140625 = 2.69140625 2.44140625 + -3.125t + t2 = 2.69140625 Factor a perfect square on the left side: (t + -1.5625)(t + -1.5625) = 2.69140625 Calculate the square root of the right side: 1.640550594 Break this problem into two subproblems by setting (t + -1.5625) equal to 1.640550594 and -1.640550594.Subproblem 1
t + -1.5625 = 1.640550594 Simplifying t + -1.5625 = 1.640550594 Reorder the terms: -1.5625 + t = 1.640550594 Solving -1.5625 + t = 1.640550594 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + t = 1.640550594 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + t = 1.640550594 + 1.5625 t = 1.640550594 + 1.5625 Combine like terms: 1.640550594 + 1.5625 = 3.203050594 t = 3.203050594 Simplifying t = 3.203050594Subproblem 2
t + -1.5625 = -1.640550594 Simplifying t + -1.5625 = -1.640550594 Reorder the terms: -1.5625 + t = -1.640550594 Solving -1.5625 + t = -1.640550594 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + t = -1.640550594 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + t = -1.640550594 + 1.5625 t = -1.640550594 + 1.5625 Combine like terms: -1.640550594 + 1.5625 = -0.078050594 t = -0.078050594 Simplifying t = -0.078050594Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.203050594, -0.078050594}Solution
t = {3.203050594, -0.078050594}
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