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Simplifying 136 = -16t2 + 136t Reorder the terms: 136 = 136t + -16t2 Solving 136 = 136t + -16t2 Solving for variable 't'. Reorder the terms: 136 + -136t + 16t2 = 136t + -136t + -16t2 + 16t2 Combine like terms: 136t + -136t = 0 136 + -136t + 16t2 = 0 + -16t2 + 16t2 136 + -136t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 136 + -136t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(17 + -17t + 2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(17 + -17t + 2t2)' equal to zero and attempt to solve: Simplifying 17 + -17t + 2t2 = 0 Solving 17 + -17t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 8.5 + -8.5t + t2 = 0 Move the constant term to the right: Add '-8.5' to each side of the equation. 8.5 + -8.5t + -8.5 + t2 = 0 + -8.5 Reorder the terms: 8.5 + -8.5 + -8.5t + t2 = 0 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + -8.5t + t2 = 0 + -8.5 -8.5t + t2 = 0 + -8.5 Combine like terms: 0 + -8.5 = -8.5 -8.5t + t2 = -8.5 The t term is -8.5t. Take half its coefficient (-4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. -8.5t + 18.0625 + t2 = -8.5 + 18.0625 Reorder the terms: 18.0625 + -8.5t + t2 = -8.5 + 18.0625 Combine like terms: -8.5 + 18.0625 = 9.5625 18.0625 + -8.5t + t2 = 9.5625 Factor a perfect square on the left side: (t + -4.25)(t + -4.25) = 9.5625 Calculate the square root of the right side: 3.092329219 Break this problem into two subproblems by setting (t + -4.25) equal to 3.092329219 and -3.092329219.Subproblem 1
t + -4.25 = 3.092329219 Simplifying t + -4.25 = 3.092329219 Reorder the terms: -4.25 + t = 3.092329219 Solving -4.25 + t = 3.092329219 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + t = 3.092329219 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + t = 3.092329219 + 4.25 t = 3.092329219 + 4.25 Combine like terms: 3.092329219 + 4.25 = 7.342329219 t = 7.342329219 Simplifying t = 7.342329219Subproblem 2
t + -4.25 = -3.092329219 Simplifying t + -4.25 = -3.092329219 Reorder the terms: -4.25 + t = -3.092329219 Solving -4.25 + t = -3.092329219 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + t = -3.092329219 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + t = -3.092329219 + 4.25 t = -3.092329219 + 4.25 Combine like terms: -3.092329219 + 4.25 = 1.157670781 t = 1.157670781 Simplifying t = 1.157670781Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.342329219, 1.157670781}Solution
t = {7.342329219, 1.157670781}
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