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Simplifying 70 = 96t + -16t2 Solving 70 = 96t + -16t2 Solving for variable 't'. Reorder the terms: 70 + -96t + 16t2 = 96t + -96t + -16t2 + 16t2 Combine like terms: 96t + -96t = 0 70 + -96t + 16t2 = 0 + -16t2 + 16t2 70 + -96t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 70 + -96t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(35 + -48t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(35 + -48t + 8t2)' equal to zero and attempt to solve: Simplifying 35 + -48t + 8t2 = 0 Solving 35 + -48t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 4.375 + -6t + t2 = 0 Move the constant term to the right: Add '-4.375' to each side of the equation. 4.375 + -6t + -4.375 + t2 = 0 + -4.375 Reorder the terms: 4.375 + -4.375 + -6t + t2 = 0 + -4.375 Combine like terms: 4.375 + -4.375 = 0.000 0.000 + -6t + t2 = 0 + -4.375 -6t + t2 = 0 + -4.375 Combine like terms: 0 + -4.375 = -4.375 -6t + t2 = -4.375 The t term is -6t. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6t + 9 + t2 = -4.375 + 9 Reorder the terms: 9 + -6t + t2 = -4.375 + 9 Combine like terms: -4.375 + 9 = 4.625 9 + -6t + t2 = 4.625 Factor a perfect square on the left side: (t + -3)(t + -3) = 4.625 Calculate the square root of the right side: 2.150581317 Break this problem into two subproblems by setting (t + -3) equal to 2.150581317 and -2.150581317.Subproblem 1
t + -3 = 2.150581317 Simplifying t + -3 = 2.150581317 Reorder the terms: -3 + t = 2.150581317 Solving -3 + t = 2.150581317 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = 2.150581317 + 3 Combine like terms: -3 + 3 = 0 0 + t = 2.150581317 + 3 t = 2.150581317 + 3 Combine like terms: 2.150581317 + 3 = 5.150581317 t = 5.150581317 Simplifying t = 5.150581317Subproblem 2
t + -3 = -2.150581317 Simplifying t + -3 = -2.150581317 Reorder the terms: -3 + t = -2.150581317 Solving -3 + t = -2.150581317 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = -2.150581317 + 3 Combine like terms: -3 + 3 = 0 0 + t = -2.150581317 + 3 t = -2.150581317 + 3 Combine like terms: -2.150581317 + 3 = 0.849418683 t = 0.849418683 Simplifying t = 0.849418683Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.150581317, 0.849418683}Solution
t = {5.150581317, 0.849418683}
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