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Simplifying 0 = -16t2 + 68t + 8 Reorder the terms: 0 = 8 + 68t + -16t2 Solving 0 = 8 + 68t + -16t2 Solving for variable 't'. Combine like terms: 0 + -8 = -8 -8 + -68t + 16t2 = 8 + 68t + -16t2 + -8 + -68t + 16t2 Reorder the terms: -8 + -68t + 16t2 = 8 + -8 + 68t + -68t + -16t2 + 16t2 Combine like terms: 8 + -8 = 0 -8 + -68t + 16t2 = 0 + 68t + -68t + -16t2 + 16t2 -8 + -68t + 16t2 = 68t + -68t + -16t2 + 16t2 Combine like terms: 68t + -68t = 0 -8 + -68t + 16t2 = 0 + -16t2 + 16t2 -8 + -68t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -8 + -68t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-2 + -17t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-2 + -17t + 4t2)' equal to zero and attempt to solve: Simplifying -2 + -17t + 4t2 = 0 Solving -2 + -17t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.5 + -4.25t + t2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -4.25t + 0.5 + t2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -4.25t + t2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -4.25t + t2 = 0 + 0.5 -4.25t + t2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -4.25t + t2 = 0.5 The t term is -4.25t. Take half its coefficient (-2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. -4.25t + 4.515625 + t2 = 0.5 + 4.515625 Reorder the terms: 4.515625 + -4.25t + t2 = 0.5 + 4.515625 Combine like terms: 0.5 + 4.515625 = 5.015625 4.515625 + -4.25t + t2 = 5.015625 Factor a perfect square on the left side: (t + -2.125)(t + -2.125) = 5.015625 Calculate the square root of the right side: 2.239559108 Break this problem into two subproblems by setting (t + -2.125) equal to 2.239559108 and -2.239559108.Subproblem 1
t + -2.125 = 2.239559108 Simplifying t + -2.125 = 2.239559108 Reorder the terms: -2.125 + t = 2.239559108 Solving -2.125 + t = 2.239559108 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + t = 2.239559108 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + t = 2.239559108 + 2.125 t = 2.239559108 + 2.125 Combine like terms: 2.239559108 + 2.125 = 4.364559108 t = 4.364559108 Simplifying t = 4.364559108Subproblem 2
t + -2.125 = -2.239559108 Simplifying t + -2.125 = -2.239559108 Reorder the terms: -2.125 + t = -2.239559108 Solving -2.125 + t = -2.239559108 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + t = -2.239559108 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + t = -2.239559108 + 2.125 t = -2.239559108 + 2.125 Combine like terms: -2.239559108 + 2.125 = -0.114559108 t = -0.114559108 Simplifying t = -0.114559108Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.364559108, -0.114559108}Solution
t = {4.364559108, -0.114559108}
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