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Simplifying 0 = -16t2 + 101t + 116 Reorder the terms: 0 = 116 + 101t + -16t2 Solving 0 = 116 + 101t + -16t2 Solving for variable 't'. Combine like terms: 0 + -116 = -116 -116 + -101t + 16t2 = 116 + 101t + -16t2 + -116 + -101t + 16t2 Reorder the terms: -116 + -101t + 16t2 = 116 + -116 + 101t + -101t + -16t2 + 16t2 Combine like terms: 116 + -116 = 0 -116 + -101t + 16t2 = 0 + 101t + -101t + -16t2 + 16t2 -116 + -101t + 16t2 = 101t + -101t + -16t2 + 16t2 Combine like terms: 101t + -101t = 0 -116 + -101t + 16t2 = 0 + -16t2 + 16t2 -116 + -101t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -116 + -101t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -7.25 + -6.3125t + t2 = 0 Move the constant term to the right: Add '7.25' to each side of the equation. -7.25 + -6.3125t + 7.25 + t2 = 0 + 7.25 Reorder the terms: -7.25 + 7.25 + -6.3125t + t2 = 0 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + -6.3125t + t2 = 0 + 7.25 -6.3125t + t2 = 0 + 7.25 Combine like terms: 0 + 7.25 = 7.25 -6.3125t + t2 = 7.25 The t term is -6.3125t. Take half its coefficient (-3.15625). Square it (9.961914063) and add it to both sides. Add '9.961914063' to each side of the equation. -6.3125t + 9.961914063 + t2 = 7.25 + 9.961914063 Reorder the terms: 9.961914063 + -6.3125t + t2 = 7.25 + 9.961914063 Combine like terms: 7.25 + 9.961914063 = 17.211914063 9.961914063 + -6.3125t + t2 = 17.211914063 Factor a perfect square on the left side: (t + -3.15625)(t + -3.15625) = 17.211914063 Calculate the square root of the right side: 4.14872439 Break this problem into two subproblems by setting (t + -3.15625) equal to 4.14872439 and -4.14872439.Subproblem 1
t + -3.15625 = 4.14872439 Simplifying t + -3.15625 = 4.14872439 Reorder the terms: -3.15625 + t = 4.14872439 Solving -3.15625 + t = 4.14872439 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.15625' to each side of the equation. -3.15625 + 3.15625 + t = 4.14872439 + 3.15625 Combine like terms: -3.15625 + 3.15625 = 0.00000 0.00000 + t = 4.14872439 + 3.15625 t = 4.14872439 + 3.15625 Combine like terms: 4.14872439 + 3.15625 = 7.30497439 t = 7.30497439 Simplifying t = 7.30497439Subproblem 2
t + -3.15625 = -4.14872439 Simplifying t + -3.15625 = -4.14872439 Reorder the terms: -3.15625 + t = -4.14872439 Solving -3.15625 + t = -4.14872439 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.15625' to each side of the equation. -3.15625 + 3.15625 + t = -4.14872439 + 3.15625 Combine like terms: -3.15625 + 3.15625 = 0.00000 0.00000 + t = -4.14872439 + 3.15625 t = -4.14872439 + 3.15625 Combine like terms: -4.14872439 + 3.15625 = -0.99247439 t = -0.99247439 Simplifying t = -0.99247439Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.30497439, -0.99247439}
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