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Simplifying 92 = 188t + -16t2 Solving 92 = 188t + -16t2 Solving for variable 't'. Reorder the terms: 92 + -188t + 16t2 = 188t + -188t + -16t2 + 16t2 Combine like terms: 188t + -188t = 0 92 + -188t + 16t2 = 0 + -16t2 + 16t2 92 + -188t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 92 + -188t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(23 + -47t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(23 + -47t + 4t2)' equal to zero and attempt to solve: Simplifying 23 + -47t + 4t2 = 0 Solving 23 + -47t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 5.75 + -11.75t + t2 = 0 Move the constant term to the right: Add '-5.75' to each side of the equation. 5.75 + -11.75t + -5.75 + t2 = 0 + -5.75 Reorder the terms: 5.75 + -5.75 + -11.75t + t2 = 0 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + -11.75t + t2 = 0 + -5.75 -11.75t + t2 = 0 + -5.75 Combine like terms: 0 + -5.75 = -5.75 -11.75t + t2 = -5.75 The t term is -11.75t. Take half its coefficient (-5.875). Square it (34.515625) and add it to both sides. Add '34.515625' to each side of the equation. -11.75t + 34.515625 + t2 = -5.75 + 34.515625 Reorder the terms: 34.515625 + -11.75t + t2 = -5.75 + 34.515625 Combine like terms: -5.75 + 34.515625 = 28.765625 34.515625 + -11.75t + t2 = 28.765625 Factor a perfect square on the left side: (t + -5.875)(t + -5.875) = 28.765625 Calculate the square root of the right side: 5.363359488 Break this problem into two subproblems by setting (t + -5.875) equal to 5.363359488 and -5.363359488.Subproblem 1
t + -5.875 = 5.363359488 Simplifying t + -5.875 = 5.363359488 Reorder the terms: -5.875 + t = 5.363359488 Solving -5.875 + t = 5.363359488 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.875' to each side of the equation. -5.875 + 5.875 + t = 5.363359488 + 5.875 Combine like terms: -5.875 + 5.875 = 0.000 0.000 + t = 5.363359488 + 5.875 t = 5.363359488 + 5.875 Combine like terms: 5.363359488 + 5.875 = 11.238359488 t = 11.238359488 Simplifying t = 11.238359488Subproblem 2
t + -5.875 = -5.363359488 Simplifying t + -5.875 = -5.363359488 Reorder the terms: -5.875 + t = -5.363359488 Solving -5.875 + t = -5.363359488 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.875' to each side of the equation. -5.875 + 5.875 + t = -5.363359488 + 5.875 Combine like terms: -5.875 + 5.875 = 0.000 0.000 + t = -5.363359488 + 5.875 t = -5.363359488 + 5.875 Combine like terms: -5.363359488 + 5.875 = 0.511640512 t = 0.511640512 Simplifying t = 0.511640512Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.238359488, 0.511640512}Solution
t = {11.238359488, 0.511640512}
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