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Simplifying 20 = 6 + 88t + 16t2 Solving 20 = 6 + 88t + 16t2 Solving for variable 't'. Combine like terms: 20 + -6 = 14 14 + -88t + -16t2 = 6 + 88t + 16t2 + -6 + -88t + -16t2 Reorder the terms: 14 + -88t + -16t2 = 6 + -6 + 88t + -88t + 16t2 + -16t2 Combine like terms: 6 + -6 = 0 14 + -88t + -16t2 = 0 + 88t + -88t + 16t2 + -16t2 14 + -88t + -16t2 = 88t + -88t + 16t2 + -16t2 Combine like terms: 88t + -88t = 0 14 + -88t + -16t2 = 0 + 16t2 + -16t2 14 + -88t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 14 + -88t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(7 + -44t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + -44t + -8t2)' equal to zero and attempt to solve: Simplifying 7 + -44t + -8t2 = 0 Solving 7 + -44t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.875 + 5.5t + t2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + 5.5t + 0.875 + t2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + 5.5t + t2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + 5.5t + t2 = 0 + 0.875 5.5t + t2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 5.5t + t2 = 0.875 The t term is 5.5t. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5t + 7.5625 + t2 = 0.875 + 7.5625 Reorder the terms: 7.5625 + 5.5t + t2 = 0.875 + 7.5625 Combine like terms: 0.875 + 7.5625 = 8.4375 7.5625 + 5.5t + t2 = 8.4375 Factor a perfect square on the left side: (t + 2.75)(t + 2.75) = 8.4375 Calculate the square root of the right side: 2.90473751 Break this problem into two subproblems by setting (t + 2.75) equal to 2.90473751 and -2.90473751.Subproblem 1
t + 2.75 = 2.90473751 Simplifying t + 2.75 = 2.90473751 Reorder the terms: 2.75 + t = 2.90473751 Solving 2.75 + t = 2.90473751 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + t = 2.90473751 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + t = 2.90473751 + -2.75 t = 2.90473751 + -2.75 Combine like terms: 2.90473751 + -2.75 = 0.15473751 t = 0.15473751 Simplifying t = 0.15473751Subproblem 2
t + 2.75 = -2.90473751 Simplifying t + 2.75 = -2.90473751 Reorder the terms: 2.75 + t = -2.90473751 Solving 2.75 + t = -2.90473751 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + t = -2.90473751 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + t = -2.90473751 + -2.75 t = -2.90473751 + -2.75 Combine like terms: -2.90473751 + -2.75 = -5.65473751 t = -5.65473751 Simplifying t = -5.65473751Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.15473751, -5.65473751}Solution
t = {0.15473751, -5.65473751}
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