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Simplifying 20 = 50t + -5t2 Solving 20 = 50t + -5t2 Solving for variable 't'. Reorder the terms: 20 + -50t + 5t2 = 50t + -50t + -5t2 + 5t2 Combine like terms: 50t + -50t = 0 20 + -50t + 5t2 = 0 + -5t2 + 5t2 20 + -50t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 20 + -50t + 5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(4 + -10t + t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(4 + -10t + t2)' equal to zero and attempt to solve: Simplifying 4 + -10t + t2 = 0 Solving 4 + -10t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -10t + -4 + t2 = 0 + -4 Reorder the terms: 4 + -4 + -10t + t2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -10t + t2 = 0 + -4 -10t + t2 = 0 + -4 Combine like terms: 0 + -4 = -4 -10t + t2 = -4 The t term is -10t. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10t + 25 + t2 = -4 + 25 Reorder the terms: 25 + -10t + t2 = -4 + 25 Combine like terms: -4 + 25 = 21 25 + -10t + t2 = 21 Factor a perfect square on the left side: (t + -5)(t + -5) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (t + -5) equal to 4.582575695 and -4.582575695.Subproblem 1
t + -5 = 4.582575695 Simplifying t + -5 = 4.582575695 Reorder the terms: -5 + t = 4.582575695 Solving -5 + t = 4.582575695 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = 4.582575695 + 5 Combine like terms: -5 + 5 = 0 0 + t = 4.582575695 + 5 t = 4.582575695 + 5 Combine like terms: 4.582575695 + 5 = 9.582575695 t = 9.582575695 Simplifying t = 9.582575695Subproblem 2
t + -5 = -4.582575695 Simplifying t + -5 = -4.582575695 Reorder the terms: -5 + t = -4.582575695 Solving -5 + t = -4.582575695 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = -4.582575695 + 5 Combine like terms: -5 + 5 = 0 0 + t = -4.582575695 + 5 t = -4.582575695 + 5 Combine like terms: -4.582575695 + 5 = 0.417424305 t = 0.417424305 Simplifying t = 0.417424305Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.582575695, 0.417424305}Solution
t = {9.582575695, 0.417424305}
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