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Simplifying 20 = 16t2 + -88t + 14 Reorder the terms: 20 = 14 + -88t + 16t2 Solving 20 = 14 + -88t + 16t2 Solving for variable 't'. Combine like terms: 20 + -14 = 6 6 + 88t + -16t2 = 14 + -88t + 16t2 + -14 + 88t + -16t2 Reorder the terms: 6 + 88t + -16t2 = 14 + -14 + -88t + 88t + 16t2 + -16t2 Combine like terms: 14 + -14 = 0 6 + 88t + -16t2 = 0 + -88t + 88t + 16t2 + -16t2 6 + 88t + -16t2 = -88t + 88t + 16t2 + -16t2 Combine like terms: -88t + 88t = 0 6 + 88t + -16t2 = 0 + 16t2 + -16t2 6 + 88t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 6 + 88t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 44t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 44t + -8t2)' equal to zero and attempt to solve: Simplifying 3 + 44t + -8t2 = 0 Solving 3 + 44t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.375 + -5.5t + t2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -5.5t + 0.375 + t2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -5.5t + t2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -5.5t + t2 = 0 + 0.375 -5.5t + t2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -5.5t + t2 = 0.375 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 = 0.375 + 7.5625 Reorder the terms: 7.5625 + -5.5t + t2 = 0.375 + 7.5625 Combine like terms: 0.375 + 7.5625 = 7.9375 7.5625 + -5.5t + t2 = 7.9375 Factor a perfect square on the left side: (t + -2.75)(t + -2.75) = 7.9375 Calculate the square root of the right side: 2.817356917 Break this problem into two subproblems by setting (t + -2.75) equal to 2.817356917 and -2.817356917.Subproblem 1
t + -2.75 = 2.817356917 Simplifying t + -2.75 = 2.817356917 Reorder the terms: -2.75 + t = 2.817356917 Solving -2.75 + t = 2.817356917 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 = 2.817356917 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + t = 2.817356917 + 2.75 t = 2.817356917 + 2.75 Combine like terms: 2.817356917 + 2.75 = 5.567356917 t = 5.567356917 Simplifying t = 5.567356917Subproblem 2
t + -2.75 = -2.817356917 Simplifying t + -2.75 = -2.817356917 Reorder the terms: -2.75 + t = -2.817356917 Solving -2.75 + t = -2.817356917 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 = -2.817356917 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + t = -2.817356917 + 2.75 t = -2.817356917 + 2.75 Combine like terms: -2.817356917 + 2.75 = -0.067356917 t = -0.067356917 Simplifying t = -0.067356917Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.567356917, -0.067356917}Solution
t = {5.567356917, -0.067356917}
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