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Simplifying -16t2 + 80t + 244 = 0 Reorder the terms: 244 + 80t + -16t2 = 0 Solving 244 + 80t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(61 + 20t + -4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(61 + 20t + -4t2)' equal to zero and attempt to solve: Simplifying 61 + 20t + -4t2 = 0 Solving 61 + 20t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -15.25 + -5t + t2 = 0 Move the constant term to the right: Add '15.25' to each side of the equation. -15.25 + -5t + 15.25 + t2 = 0 + 15.25 Reorder the terms: -15.25 + 15.25 + -5t + t2 = 0 + 15.25 Combine like terms: -15.25 + 15.25 = 0.00 0.00 + -5t + t2 = 0 + 15.25 -5t + t2 = 0 + 15.25 Combine like terms: 0 + 15.25 = 15.25 -5t + t2 = 15.25 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 = 15.25 + 6.25 Reorder the terms: 6.25 + -5t + t2 = 15.25 + 6.25 Combine like terms: 15.25 + 6.25 = 21.5 6.25 + -5t + t2 = 21.5 Factor a perfect square on the left side: (t + -2.5)(t + -2.5) = 21.5 Calculate the square root of the right side: 4.636809248 Break this problem into two subproblems by setting (t + -2.5) equal to 4.636809248 and -4.636809248.Subproblem 1
t + -2.5 = 4.636809248 Simplifying t + -2.5 = 4.636809248 Reorder the terms: -2.5 + t = 4.636809248 Solving -2.5 + t = 4.636809248 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 = 4.636809248 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = 4.636809248 + 2.5 t = 4.636809248 + 2.5 Combine like terms: 4.636809248 + 2.5 = 7.136809248 t = 7.136809248 Simplifying t = 7.136809248Subproblem 2
t + -2.5 = -4.636809248 Simplifying t + -2.5 = -4.636809248 Reorder the terms: -2.5 + t = -4.636809248 Solving -2.5 + t = -4.636809248 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 = -4.636809248 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = -4.636809248 + 2.5 t = -4.636809248 + 2.5 Combine like terms: -4.636809248 + 2.5 = -2.136809248 t = -2.136809248 Simplifying t = -2.136809248Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.136809248, -2.136809248}Solution
t = {7.136809248, -2.136809248}
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