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Simplifying 80 = -5t2 + 100t Reorder the terms: 80 = 100t + -5t2 Solving 80 = 100t + -5t2 Solving for variable 't'. Reorder the terms: 80 + -100t + 5t2 = 100t + -100t + -5t2 + 5t2 Combine like terms: 100t + -100t = 0 80 + -100t + 5t2 = 0 + -5t2 + 5t2 80 + -100t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 80 + -100t + 5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(16 + -20t + t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(16 + -20t + t2)' equal to zero and attempt to solve: Simplifying 16 + -20t + t2 = 0 Solving 16 + -20t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + -20t + -16 + t2 = 0 + -16 Reorder the terms: 16 + -16 + -20t + t2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -20t + t2 = 0 + -16 -20t + t2 = 0 + -16 Combine like terms: 0 + -16 = -16 -20t + t2 = -16 The t term is -20t. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20t + 100 + t2 = -16 + 100 Reorder the terms: 100 + -20t + t2 = -16 + 100 Combine like terms: -16 + 100 = 84 100 + -20t + t2 = 84 Factor a perfect square on the left side: (t + -10)(t + -10) = 84 Calculate the square root of the right side: 9.16515139 Break this problem into two subproblems by setting (t + -10) equal to 9.16515139 and -9.16515139.Subproblem 1
t + -10 = 9.16515139 Simplifying t + -10 = 9.16515139 Reorder the terms: -10 + t = 9.16515139 Solving -10 + t = 9.16515139 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + t = 9.16515139 + 10 Combine like terms: -10 + 10 = 0 0 + t = 9.16515139 + 10 t = 9.16515139 + 10 Combine like terms: 9.16515139 + 10 = 19.16515139 t = 19.16515139 Simplifying t = 19.16515139Subproblem 2
t + -10 = -9.16515139 Simplifying t + -10 = -9.16515139 Reorder the terms: -10 + t = -9.16515139 Solving -10 + t = -9.16515139 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + t = -9.16515139 + 10 Combine like terms: -10 + 10 = 0 0 + t = -9.16515139 + 10 t = -9.16515139 + 10 Combine like terms: -9.16515139 + 10 = 0.83484861 t = 0.83484861 Simplifying t = 0.83484861Solution
The solution to the problem is based on the solutions from the subproblems. t = {19.16515139, 0.83484861}Solution
t = {19.16515139, 0.83484861}
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