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Simplifying 60 = 80t + -16t2 Solving 60 = 80t + -16t2 Solving for variable 't'. Reorder the terms: 60 + -80t + 16t2 = 80t + -80t + -16t2 + 16t2 Combine like terms: 80t + -80t = 0 60 + -80t + 16t2 = 0 + -16t2 + 16t2 60 + -80t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 60 + -80t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(15 + -20t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(15 + -20t + 4t2)' equal to zero and attempt to solve: Simplifying 15 + -20t + 4t2 = 0 Solving 15 + -20t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.75 + -5t + t2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + -5t + -3.75 + t2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + -5t + t2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + -5t + t2 = 0 + -3.75 -5t + t2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 -5t + t2 = -3.75 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 = -3.75 + 6.25 Reorder the terms: 6.25 + -5t + t2 = -3.75 + 6.25 Combine like terms: -3.75 + 6.25 = 2.5 6.25 + -5t + t2 = 2.5 Factor a perfect square on the left side: (t + -2.5)(t + -2.5) = 2.5 Calculate the square root of the right side: 1.58113883 Break this problem into two subproblems by setting (t + -2.5) equal to 1.58113883 and -1.58113883.Subproblem 1
t + -2.5 = 1.58113883 Simplifying t + -2.5 = 1.58113883 Reorder the terms: -2.5 + t = 1.58113883 Solving -2.5 + t = 1.58113883 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 = 1.58113883 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = 1.58113883 + 2.5 t = 1.58113883 + 2.5 Combine like terms: 1.58113883 + 2.5 = 4.08113883 t = 4.08113883 Simplifying t = 4.08113883Subproblem 2
t + -2.5 = -1.58113883 Simplifying t + -2.5 = -1.58113883 Reorder the terms: -2.5 + t = -1.58113883 Solving -2.5 + t = -1.58113883 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 = -1.58113883 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = -1.58113883 + 2.5 t = -1.58113883 + 2.5 Combine like terms: -1.58113883 + 2.5 = 0.91886117 t = 0.91886117 Simplifying t = 0.91886117Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.08113883, 0.91886117}Solution
t = {4.08113883, 0.91886117}
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