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Simplifying 16t2 + 80t + 60 = 0 Reorder the terms: 60 + 80t + 16t2 = 0 Solving 60 + 80t + 16t2 = 0 Solving for variable 't'. 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 = -0.91886117 t = -0.91886117 Simplifying t = -0.91886117Subproblem 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 = -4.08113883 t = -4.08113883 Simplifying t = -4.08113883Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.91886117, -4.08113883}Solution
t = {-0.91886117, -4.08113883}
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