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Simplifying 80 = -16t2 + 100t Reorder the terms: 80 = 100t + -16t2 Solving 80 = 100t + -16t2 Solving for variable 't'. Reorder the terms: 80 + -100t + 16t2 = 100t + -100t + -16t2 + 16t2 Combine like terms: 100t + -100t = 0 80 + -100t + 16t2 = 0 + -16t2 + 16t2 80 + -100t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 80 + -100t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(20 + -25t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(20 + -25t + 4t2)' equal to zero and attempt to solve: Simplifying 20 + -25t + 4t2 = 0 Solving 20 + -25t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 5 + -6.25t + t2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -6.25t + -5 + t2 = 0 + -5 Reorder the terms: 5 + -5 + -6.25t + t2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6.25t + t2 = 0 + -5 -6.25t + t2 = 0 + -5 Combine like terms: 0 + -5 = -5 -6.25t + t2 = -5 The t term is -6.25t. Take half its coefficient (-3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. -6.25t + 9.765625 + t2 = -5 + 9.765625 Reorder the terms: 9.765625 + -6.25t + t2 = -5 + 9.765625 Combine like terms: -5 + 9.765625 = 4.765625 9.765625 + -6.25t + t2 = 4.765625 Factor a perfect square on the left side: (t + -3.125)(t + -3.125) = 4.765625 Calculate the square root of the right side: 2.18303115 Break this problem into two subproblems by setting (t + -3.125) equal to 2.18303115 and -2.18303115.Subproblem 1
t + -3.125 = 2.18303115 Simplifying t + -3.125 = 2.18303115 Reorder the terms: -3.125 + t = 2.18303115 Solving -3.125 + t = 2.18303115 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + t = 2.18303115 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + t = 2.18303115 + 3.125 t = 2.18303115 + 3.125 Combine like terms: 2.18303115 + 3.125 = 5.30803115 t = 5.30803115 Simplifying t = 5.30803115Subproblem 2
t + -3.125 = -2.18303115 Simplifying t + -3.125 = -2.18303115 Reorder the terms: -3.125 + t = -2.18303115 Solving -3.125 + t = -2.18303115 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + t = -2.18303115 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + t = -2.18303115 + 3.125 t = -2.18303115 + 3.125 Combine like terms: -2.18303115 + 3.125 = 0.94196885 t = 0.94196885 Simplifying t = 0.94196885Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.30803115, 0.94196885}Solution
t = {5.30803115, 0.94196885}
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