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Simplifying 92 = 164t + -16t2 Solving 92 = 164t + -16t2 Solving for variable 't'. Reorder the terms: 92 + -164t + 16t2 = 164t + -164t + -16t2 + 16t2 Combine like terms: 164t + -164t = 0 92 + -164t + 16t2 = 0 + -16t2 + 16t2 92 + -164t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 92 + -164t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(23 + -41t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(23 + -41t + 4t2)' equal to zero and attempt to solve: Simplifying 23 + -41t + 4t2 = 0 Solving 23 + -41t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 5.75 + -10.25t + t2 = 0 Move the constant term to the right: Add '-5.75' to each side of the equation. 5.75 + -10.25t + -5.75 + t2 = 0 + -5.75 Reorder the terms: 5.75 + -5.75 + -10.25t + t2 = 0 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + -10.25t + t2 = 0 + -5.75 -10.25t + t2 = 0 + -5.75 Combine like terms: 0 + -5.75 = -5.75 -10.25t + t2 = -5.75 The t term is -10.25t. Take half its coefficient (-5.125). Square it (26.265625) and add it to both sides. Add '26.265625' to each side of the equation. -10.25t + 26.265625 + t2 = -5.75 + 26.265625 Reorder the terms: 26.265625 + -10.25t + t2 = -5.75 + 26.265625 Combine like terms: -5.75 + 26.265625 = 20.515625 26.265625 + -10.25t + t2 = 20.515625 Factor a perfect square on the left side: (t + -5.125)(t + -5.125) = 20.515625 Calculate the square root of the right side: 4.529417733 Break this problem into two subproblems by setting (t + -5.125) equal to 4.529417733 and -4.529417733.Subproblem 1
t + -5.125 = 4.529417733 Simplifying t + -5.125 = 4.529417733 Reorder the terms: -5.125 + t = 4.529417733 Solving -5.125 + t = 4.529417733 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.125' to each side of the equation. -5.125 + 5.125 + t = 4.529417733 + 5.125 Combine like terms: -5.125 + 5.125 = 0.000 0.000 + t = 4.529417733 + 5.125 t = 4.529417733 + 5.125 Combine like terms: 4.529417733 + 5.125 = 9.654417733 t = 9.654417733 Simplifying t = 9.654417733Subproblem 2
t + -5.125 = -4.529417733 Simplifying t + -5.125 = -4.529417733 Reorder the terms: -5.125 + t = -4.529417733 Solving -5.125 + t = -4.529417733 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.125' to each side of the equation. -5.125 + 5.125 + t = -4.529417733 + 5.125 Combine like terms: -5.125 + 5.125 = 0.000 0.000 + t = -4.529417733 + 5.125 t = -4.529417733 + 5.125 Combine like terms: -4.529417733 + 5.125 = 0.595582267 t = 0.595582267 Simplifying t = 0.595582267Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.654417733, 0.595582267}Solution
t = {9.654417733, 0.595582267}
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