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Simplifying 8 + 40.8t + -16t2 = 10 Solving 8 + 40.8t + -16t2 = 10 Solving for variable 't'. Reorder the terms: 8 + -10 + 40.8t + -16t2 = 10 + -10 Combine like terms: 8 + -10 = -2 -2 + 40.8t + -16t2 = 10 + -10 Combine like terms: 10 + -10 = 0 -2 + 40.8t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 0.125 + -2.55t + t2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + -2.55t + -0.125 + t2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + -2.55t + t2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + -2.55t + t2 = 0 + -0.125 -2.55t + t2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 -2.55t + t2 = -0.125 The t term is -2.55t. Take half its coefficient (-1.275). Square it (1.625625) and add it to both sides. Add '1.625625' to each side of the equation. -2.55t + 1.625625 + t2 = -0.125 + 1.625625 Reorder the terms: 1.625625 + -2.55t + t2 = -0.125 + 1.625625 Combine like terms: -0.125 + 1.625625 = 1.500625 1.625625 + -2.55t + t2 = 1.500625 Factor a perfect square on the left side: (t + -1.275)(t + -1.275) = 1.500625 Calculate the square root of the right side: 1.225 Break this problem into two subproblems by setting (t + -1.275) equal to 1.225 and -1.225.Subproblem 1
t + -1.275 = 1.225 Simplifying t + -1.275 = 1.225 Reorder the terms: -1.275 + t = 1.225 Solving -1.275 + t = 1.225 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.275' to each side of the equation. -1.275 + 1.275 + t = 1.225 + 1.275 Combine like terms: -1.275 + 1.275 = 0.000 0.000 + t = 1.225 + 1.275 t = 1.225 + 1.275 Combine like terms: 1.225 + 1.275 = 2.5 t = 2.5 Simplifying t = 2.5Subproblem 2
t + -1.275 = -1.225 Simplifying t + -1.275 = -1.225 Reorder the terms: -1.275 + t = -1.225 Solving -1.275 + t = -1.225 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.275' to each side of the equation. -1.275 + 1.275 + t = -1.225 + 1.275 Combine like terms: -1.275 + 1.275 = 0.000 0.000 + t = -1.225 + 1.275 t = -1.225 + 1.275 Combine like terms: -1.225 + 1.275 = 0.05 t = 0.05 Simplifying t = 0.05Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.5, 0.05}
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