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Simplifying 0 = -16t2 + -8t + 20 Reorder the terms: 0 = 20 + -8t + -16t2 Solving 0 = 20 + -8t + -16t2 Solving for variable 't'. Combine like terms: 0 + -20 = -20 -20 + 8t + 16t2 = 20 + -8t + -16t2 + -20 + 8t + 16t2 Reorder the terms: -20 + 8t + 16t2 = 20 + -20 + -8t + 8t + -16t2 + 16t2 Combine like terms: 20 + -20 = 0 -20 + 8t + 16t2 = 0 + -8t + 8t + -16t2 + 16t2 -20 + 8t + 16t2 = -8t + 8t + -16t2 + 16t2 Combine like terms: -8t + 8t = 0 -20 + 8t + 16t2 = 0 + -16t2 + 16t2 -20 + 8t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -20 + 8t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-5 + 2t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + 2t + 4t2)' equal to zero and attempt to solve: Simplifying -5 + 2t + 4t2 = 0 Solving -5 + 2t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + 0.5t + t2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 0.5t + 1.25 + t2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 0.5t + t2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 0.5t + t2 = 0 + 1.25 0.5t + t2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 0.5t + t2 = 1.25 The t term is 0.5t. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5t + 0.0625 + t2 = 1.25 + 0.0625 Reorder the terms: 0.0625 + 0.5t + t2 = 1.25 + 0.0625 Combine like terms: 1.25 + 0.0625 = 1.3125 0.0625 + 0.5t + t2 = 1.3125 Factor a perfect square on the left side: (t + 0.25)(t + 0.25) = 1.3125 Calculate the square root of the right side: 1.145643924 Break this problem into two subproblems by setting (t + 0.25) equal to 1.145643924 and -1.145643924.Subproblem 1
t + 0.25 = 1.145643924 Simplifying t + 0.25 = 1.145643924 Reorder the terms: 0.25 + t = 1.145643924 Solving 0.25 + t = 1.145643924 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + t = 1.145643924 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + t = 1.145643924 + -0.25 t = 1.145643924 + -0.25 Combine like terms: 1.145643924 + -0.25 = 0.895643924 t = 0.895643924 Simplifying t = 0.895643924Subproblem 2
t + 0.25 = -1.145643924 Simplifying t + 0.25 = -1.145643924 Reorder the terms: 0.25 + t = -1.145643924 Solving 0.25 + t = -1.145643924 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + t = -1.145643924 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + t = -1.145643924 + -0.25 t = -1.145643924 + -0.25 Combine like terms: -1.145643924 + -0.25 = -1.395643924 t = -1.395643924 Simplifying t = -1.395643924Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.895643924, -1.395643924}Solution
t = {0.895643924, -1.395643924}
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