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Simplifying t = -16t2 + 30t + 8 Reorder the terms: t = 8 + 30t + -16t2 Solving t = 8 + 30t + -16t2 Solving for variable 't'. Reorder the terms: -8 + t + -30t + 16t2 = 8 + 30t + -16t2 + -8 + -30t + 16t2 Combine like terms: t + -30t = -29t -8 + -29t + 16t2 = 8 + 30t + -16t2 + -8 + -30t + 16t2 Reorder the terms: -8 + -29t + 16t2 = 8 + -8 + 30t + -30t + -16t2 + 16t2 Combine like terms: 8 + -8 = 0 -8 + -29t + 16t2 = 0 + 30t + -30t + -16t2 + 16t2 -8 + -29t + 16t2 = 30t + -30t + -16t2 + 16t2 Combine like terms: 30t + -30t = 0 -8 + -29t + 16t2 = 0 + -16t2 + 16t2 -8 + -29t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -8 + -29t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.5 + -1.8125t + t2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -1.8125t + 0.5 + t2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -1.8125t + t2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -1.8125t + t2 = 0 + 0.5 -1.8125t + t2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -1.8125t + t2 = 0.5 The t term is -1.8125t. Take half its coefficient (-0.90625). Square it (0.8212890625) and add it to both sides. Add '0.8212890625' to each side of the equation. -1.8125t + 0.8212890625 + t2 = 0.5 + 0.8212890625 Reorder the terms: 0.8212890625 + -1.8125t + t2 = 0.5 + 0.8212890625 Combine like terms: 0.5 + 0.8212890625 = 1.3212890625 0.8212890625 + -1.8125t + t2 = 1.3212890625 Factor a perfect square on the left side: (t + -0.90625)(t + -0.90625) = 1.3212890625 Calculate the square root of the right side: 1.149473385 Break this problem into two subproblems by setting (t + -0.90625) equal to 1.149473385 and -1.149473385.Subproblem 1
t + -0.90625 = 1.149473385 Simplifying t + -0.90625 = 1.149473385 Reorder the terms: -0.90625 + t = 1.149473385 Solving -0.90625 + t = 1.149473385 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.90625' to each side of the equation. -0.90625 + 0.90625 + t = 1.149473385 + 0.90625 Combine like terms: -0.90625 + 0.90625 = 0.00000 0.00000 + t = 1.149473385 + 0.90625 t = 1.149473385 + 0.90625 Combine like terms: 1.149473385 + 0.90625 = 2.055723385 t = 2.055723385 Simplifying t = 2.055723385Subproblem 2
t + -0.90625 = -1.149473385 Simplifying t + -0.90625 = -1.149473385 Reorder the terms: -0.90625 + t = -1.149473385 Solving -0.90625 + t = -1.149473385 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.90625' to each side of the equation. -0.90625 + 0.90625 + t = -1.149473385 + 0.90625 Combine like terms: -0.90625 + 0.90625 = 0.00000 0.00000 + t = -1.149473385 + 0.90625 t = -1.149473385 + 0.90625 Combine like terms: -1.149473385 + 0.90625 = -0.243223385 t = -0.243223385 Simplifying t = -0.243223385Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.055723385, -0.243223385}
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