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Simplifying 90 = 80t + -16t2 Solving 90 = 80t + -16t2 Solving for variable 't'. Reorder the terms: 90 + -80t + 16t2 = 80t + -80t + -16t2 + 16t2 Combine like terms: 80t + -80t = 0 90 + -80t + 16t2 = 0 + -16t2 + 16t2 90 + -80t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 90 + -80t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(45 + -40t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(45 + -40t + 8t2)' equal to zero and attempt to solve: Simplifying 45 + -40t + 8t2 = 0 Solving 45 + -40t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 5.625 + -5t + t2 = 0 Move the constant term to the right: Add '-5.625' to each side of the equation. 5.625 + -5t + -5.625 + t2 = 0 + -5.625 Reorder the terms: 5.625 + -5.625 + -5t + t2 = 0 + -5.625 Combine like terms: 5.625 + -5.625 = 0.000 0.000 + -5t + t2 = 0 + -5.625 -5t + t2 = 0 + -5.625 Combine like terms: 0 + -5.625 = -5.625 -5t + t2 = -5.625 The t term is -5t. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5t + 6.25 + t2 = -5.625 + 6.25 Reorder the terms: 6.25 + -5t + t2 = -5.625 + 6.25 Combine like terms: -5.625 + 6.25 = 0.625 6.25 + -5t + t2 = 0.625 Factor a perfect square on the left side: (t + -2.5)(t + -2.5) = 0.625 Calculate the square root of the right side: 0.790569415 Break this problem into two subproblems by setting (t + -2.5) equal to 0.790569415 and -0.790569415.Subproblem 1
t + -2.5 = 0.790569415 Simplifying t + -2.5 = 0.790569415 Reorder the terms: -2.5 + t = 0.790569415 Solving -2.5 + t = 0.790569415 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = 0.790569415 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = 0.790569415 + 2.5 t = 0.790569415 + 2.5 Combine like terms: 0.790569415 + 2.5 = 3.290569415 t = 3.290569415 Simplifying t = 3.290569415Subproblem 2
t + -2.5 = -0.790569415 Simplifying t + -2.5 = -0.790569415 Reorder the terms: -2.5 + t = -0.790569415 Solving -2.5 + t = -0.790569415 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = -0.790569415 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = -0.790569415 + 2.5 t = -0.790569415 + 2.5 Combine like terms: -0.790569415 + 2.5 = 1.709430585 t = 1.709430585 Simplifying t = 1.709430585Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.290569415, 1.709430585}Solution
t = {3.290569415, 1.709430585}
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